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Standard XII

Mathematics

Sum of n Terms

a, b, c are r...

Question

a, b, c are real numbers in the polynomial $P (Z) = 2 Z^{4} + a Z^{3} + b Z^{2} c Z + 3$ . If two roots of the equation P(Z) = 0 are 2 and i, then find the value 'a'.

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Solution

Let roots are $2, i, - i, x$ (let)
Products $= 2. i . (- i) . x = 3 ⟹ 2 x = 3 ⟹ x = 3 / 2$
sum of roots are $2 + \frac{3}{2} = 7 / 2$
$a = - 7 / 2$

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Similar questions

Q. a, b, c are real numbers in the polynomial , P(z) =

2 z^{4} + a z^{3} + b z^{2} + c z + 3

. If two roots of the equations P(z) = 0 are 2 and i. Then which of the following are true.

$P (z) = z^{4} + a z^{3} + b z^{2} + c z + d$ is a polynomial where a, b, c and d are real numbers. Find $a + b + c + d$ if two zeros of polynomial P are the following complex numbers: $2 - i$ and $1 - i$ .

Q. Let

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The value of

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a ε R

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a, b, c are real numbers in the polynomial P(Z)=2Z4+aZ3+bZ2cZ+3. If two roots of the equation P(Z) = 0 are 2 and i, then find the value 'a'.

Let roots are 2,i,−i,x(let)Products =2.i.(−i).x=3⟹2x=3⟹x=3/2sum of roots are 2+32=7/2a=−7/2

a, b, c are real numbers in the polynomial $P (Z) = 2 Z^{4} + a Z^{3} + b Z^{2} c Z + 3$ . If two roots of the equation P(Z) = 0 are 2 and i, then find the value 'a'.

Let roots are $2, i, - i, x$ (let)
Products $= 2. i . (- i) . x = 3 ⟹ 2 x = 3 ⟹ x = 3 / 2$
sum of roots are $2 + \frac{3}{2} = 7 / 2$
$a = - 7 / 2$