Question

If the sum of the square of zeroes of a quadratic polynomial f(x)=x² -8x+k is 40, find the value of k.

Answer 1

SOLUTION:-

Given:

If the sum of the square of zeroes of a quadratic polynomial f(x) x² -8x +k is 40.

To find:

The value of k.

Explanation:

We have,

f(x)= x²-8x +k

• A= 1
• B= -8
• C= k

Sum of the zeroes of the quadratic polynomial:

$\alpha + \beta = \frac{ - b}{a}$

So,

$\alpha + \beta = - ( \frac{ - 8}{1} ) \\ \\ \alpha + \beta = 8$

&

Product of zeroes of the quadratic polynomial:

$\alpha \beta = \frac{c}{a} \\ \\ \alpha \beta = \frac{k}{1} \\ \\ \alpha \beta = k$

• According to the question:

$\alpha {}^{2} + { \beta }^{2} = 40 \\ \\ ( \alpha + \beta ) {}^{2} - 2 \alpha \beta = 40 \\ \\ ( {8)}^{2} - 2k = 40 \\ \\ 64 - 2k = 40 \\ \\ - 2k = 40 - 64 \\ \\ - 2 k = - 24 \\ \\ 2k = 24 \\ \\ k = \frac{24}{2} \\ \\ k = 12$

Thus,

The value of k is 12.