Question

sum of the zeroes of polynomial p(x)=X2-kx+9 is 7 find value of k​

Answer 1

The value of k = 7

Given :

The polynomial p(x) = x² - kx + 9

Sum of the zeroes of the polynomial is 7

To find :

The value of k

Concept :

If $\sf \alpha \: \: and \: \: \beta \:$are the zeroes of the quadratic equation $\sf{ a {x}^{2} + bx + c= 0}$

Then

$\displaystyle \sf \alpha + \beta \: = - \frac{b}{a} \: \: and \: \: \: \alpha \beta \: = \frac{c}{a}$

Solution :

Step 1 of 2 :

Write down the given polynomial

Here the given polynomial is

p(x) = x² - kx + 9

Comparing with the general quadratic polynomial p(x) = ax² + bx + c we get a = 1 , b = - k , c = 9

Step 2 of 2 :

Find the value of k

Here it is given that Sum of the zeroes of the polynomial is 7

$\displaystyle \sf{ Sum \: of \: the \: zeroes = - \frac{b}{a} }$

$\displaystyle \sf{ \implies 7 = - \frac{ - k}{1} }$

$\displaystyle \sf{ \implies 7 = k}$

$\displaystyle \sf{ \implies k = 7}$

Hence the value of k = 7

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