Let a, B and y be the roots of the equation 523 + 22 + 3z + 4 = 0. Find the values of the following: (a) a2 + B2 + ². 1 B – 1 (b) a + 1 7 - 1 r +1 B+1

Q: Given that a, B and y are the roots of the equation 423 – 522 + 3z + 11 = 0. a3 Without finding a, B…

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Q: If the roots of the equation ax²+bx +c = 0 be a and s and those of the equation b - 4ac Ax + Bx +C =…

A: Introduction :

Q: If 1/2 is a root of the equation x2+kx-(5/4) = 0 , then find the value of k

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Q: Find all the solutions of + 1z10 + 122 +...+11 = 0 to: Hint: What happens when you multiply the…

A: We will find out the required roots.

Q: If the roots of the equation x - 8x + a² - 6a = distinct, then find all possible values of a.

A: Since the roots of the given equation are real and distinct, We must have…

Q: Determine all the roots of R(y)=12y²+11y-5

A: R(y)=12y²+11y-5

Q: Determine the nature of the roots of the following equations: (a) 3x + 5x + 4 = 0 (c) x-8x + 16 = 0…

A: Since you have asked multiple subparts, we will solve the first three question for you. . If you…

Q: If x^4+ax^2+bx+c= 0 has roots x=−1,2,and 3, find the values of a, b,and c, as well as the fourth…

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Q: I Without solving, find the sum and product of the roots of each of the followine equations. 1. 4x…

A: As per the company guidelines we are supposed to answer the first question of first 5…

Q: If the sum of the roots of the equation 1/(x+ a) + 1/(x + b) = 1/c is zero, then prove that the…

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Q: Find all real solutions of the equation 7n2=28.

A: Consider the given equation.

Q: 4. If A is the set of roots of the equation x³ – 3x + 2 = 0, then A is equal to a) {1; –3; 2} b)…

A: We have to find the roots of the given equation. To find roots of this equation we are going to…

Q: If r; and r, are the roots of equation x² – 2x+4 =0, then find Er .

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Q: If a, b, and c are in A.P. and one root of the equation is 2, then find the other root. ax²+bx+c=0

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Q: If a, b, c are in GP, then the equations ax² + 2bx + c = 0 and dx² + 2ex + f = 0 have a common root…

A: Given a,b,c are in g.p So the ratio will be same ba=cbb2=acb=ac ---- {1}

Q: If r1 and r2 are two real and unequal roots to the auxiliaryequation ar2 + br + c = 0 , then general…

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Q: Let ne Z and AABC be a right triangle with right angle at C. If sin A and sin B are the roots of the…

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Q: If (2+3) is one of the roots of the equation x² + (α-ix+bi=o find the valus of a b

A: given  one of the root of the equation x2+(a-i)x+bi=0 is 2+3i we have to find the value of a, b…

Q: Find the value of p for which the roots of the equation px(x-2)+6=0 are equal

A: Given the equation px(x-2)+6=0. We need to find the value of p for which the roots of the equation…

Q: 12. For what values of k, will the equation 3x? +4x + k = 0 have two equal roots?

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Q: Prove that the equation x2(a2+b2)+2x(ac+bd)+(c2+d2)=0 has no real root ,if ad is not equals to bc

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Q: For which values of k will the equation ×^2-5×-k=0 have equal roots

A: Consider the given equation. x2-5x-k=0 For the equal the root of the equation, the discriminant will…

Q: Determine the nature of the roots of the following equations: (a) 3x +5x + 4 = 0 (c) x-8x+ 16 = 0…

A: “Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: Find the roots of the equation z³ – 1 = 0.

A: Given,           z3-1=0

Q: E(x)=x+4x³+2x²+20x–15, and one of the roots is 5 i.

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Q: For what value of k does the equation kx2 -4x + k = 0 has two equal real roots?

A: Given, kx²-4x+k=0 a=k b=-4 c=k

Q: If 7, and r, are the roots of equationx -2x+4=0, then find r.

A: Given equation, x2-2x+4=0 If r1 and r2 are the roots of the equation, then find ∑ri3.

Q: Find all the roots of z = -4 + (4V3)i giving each root in the form re". %3D 8° = -4+ (43) C

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Q: 2D4-4D³-23D² + 12D + 36 = 0

A: Given auxiliary equation is 2D4-4D3-23D2+12D+36=0 Now we replace D by x f(x)=2x4-4x3-23x2+12x+36…

Q: 13. Find the roots of the equation x+9x+ 18-0. A. 3 or 6 B. 3 or-6 C.-3 or 6 D.-3 or -6

A: As per guidelines, We’ll answer the first question since the exact one wasn’t specified. Please…

Q: If the sum of the roots of the equation 1/(x + a) + 1/(x + b) 1/c is zero, then prove that the…

A: Given that if the sum of the roots of the equation                   1x+a+1x+b=1c, is zero. To prove…

Q: Given that 3+2i is a root of the equation x^4-8x^3+30x^2-56x+65=0.Which of the following quadratic…

A: Given: 3+2i  is a root of the equation:  x4-8x3+30x2-56x+65=0

Q: Determine all the roots of R(y)=12y²+11y-5.

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Q: The roots of the equation D(4) – 81y = 0 are

A: Here I am attaching image so that you understand each and every step.

Q: Identify the roots for the equation 5 x 2 + 2 x = -4. -1+iv19 | 10 iv19

A: Given, 5x²+2x+4= 0 We know that, The standard quadratic equation is given by, ax²+bx+c=0. Here, a=5…

Q: Find the roots of: (D² - 4) (D2)y = 0

A: To find the roots of the given equation D2-4(D-2)y=0

Q: 1, Without solving, find the sum and product of the roots of each of the following equations. 1.…

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Q: If the roots of equation x² - 2cx + ab = 0 are real and unequal, then prove that the roots of x²…

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Q: Let A and B be real numbers such that a root of the equation z ^ 3 + Az ^ 2 + Bz + 26 = 0 is 1 + i.…

A: First of all, as coefficients A and B are real, we know that, if z ∈ C is a root of an equation,…

Q: Given that k#1 and the roots of the equation z' = k are à, B (x-2) and Y, use the substitution z =…

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Q: If a, b, c are in GP and the equation ax² +2bx+c= 0 and dx² +2ex+f=0 have a common root, then is it…

A: Given that a,b,c in G.P and the equation ax2+2bx+c=0 and dx2+2ex+f=0 have a common root.

Q: b) Find all the roots of x3+7x?+7x+1=D0

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Q: If a, b are the roots of x2 + px + 1 = 0 and c, d are the roots а, of x? + qx + 1 = 0, then the…

A: Introduction :

Q: The real roots of the equation 7o97(«²-4x+5) = x-1 are-

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Q: Find all roots: 4- V-7+24i

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Q: 17. {7 + 3i}

A: Given, f(x)=ax2+bx+c roots of equation are, we know from the propert of roots,

Q: If a and B are the roots of the equation x² - 3x + 4 = 0, the equation whose roots are a? + a + 1…

A: Since you have asked multiple questions in a single request we would be answering only the first…