Question

if alpha +beta=40 for f(x)=x2-8x+k, find the value of k​

Answer 1

Question :

If $\alpha \beta = 40$ for f(x) = x² - 8x + k, Find the value of k.

Solution :

For a quadratic polynomial ax² + bx + c with roots $\alpha$ , $\beta$

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

Product of roots $\alpha \beta = \frac{c}{a}$

Given quadratic polynomial,

f(x) = x² - 8x + k

Comparing with ax² + bx + c,

• a = 1
• b = - 8
• c = k

Also given,

$\boxed{\alpha \beta = 40}$

But,

$\boxed{\alpha \beta = \frac{c}{a}}$

So,

$\boxed{ \frac{c}{a} = 40}$

Substituting the values :

$\boxed{\frac{k}{1} = 40}$

Therefore,

$\boxed{\pink{k = 40}}$

Note :

$\alpha\:+\:\beta$ can't be 40 for the given polynomial because,

Sum of roots = - b/a = - (-8)/1 = 8 and not 40.

Answer 2

Answer:

GIVEN :-

F(x) = x^2-8x+k

Sum of the roots = 40 ( but it is wrong )

REQUIRED TO GET :-

Value of k = ?

NOTE :-

• If ax^2+bx+c is a quadratic equation then product of roots = c/a
• Here in the question the given sum of the roots is wrong it is the product of the roots

SOLUTION :-

Here ,

• a = 1
• b = -8
• c = k

So,

$product \: of \: roots \: = \frac{c}{a} \\ \\ = \frac{k}{1} \\ \\ = 40$

THEREFORE THE REQUIRED ANSWER IS K = 40

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