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Relationship between Zeroes and Coefficients of a Polynomial

If the roots ...

Question

If the roots of the equation $2 x^{2} - 5 x + c = 0$ , $a, b$ are in the ratio of $2 : 3$ , then find the value of b?

2

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3

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4

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6

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Solution

The correct option is D $3$
Let the roots of the equation $2 a$ and $3 a$ respectively.
$2 a + 3 a = 5 a$ = $- \frac{- 5}{2}$
= $\frac{5}{2}$
= $a = \frac{1}{2}$
Product of the roots: $6 a^{2} = b / 2$ =
$b = 12 a^{2}$
$a = \frac{1}{2}$ , $b = 3$

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