The zeroes of a polynomial are twice the zeroes of the polynomial . The value of p is

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Solution

Q.
The zeroes of a polynomial $x^{2} + p x + q$ are twice the zeroes of the polynomial $4 x^{2} - 5 x - 6$ . The value of p is :

1 $- 5 / 2$

2 $5 / 2$

3 $- 5$

4 $10$

Ans.
(1)

Given polynomials : $x^{2} + p x + q$ ...(i)

and $4 x^{2} - 5 x - 6$ ...(ii)

Zero of polynomial $4 x^{2} - 5 x - 6$ are: $x = 2$ and $x = - 3 / 4$

Now, zero of polynomial $x^{2} + p x + q$ are 4 and $- 3 / 2$

$∴$ Sum of zeroes $= - \frac{p}{1}$

$\Rightarrow 4 - \frac{3}{2} = - \frac{p}{1} \Rightarrow - p = \frac{5}{2} \Rightarrow p = - \frac{5}{2}$

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