Question

If a and b are the zeros of the quadratic polynomial kx2+4x+4 such that a2+b2=24 find the value of k

Answer 1

Plz c the attachment

Answer 2

The value of k is $-1, \frac{2}{3}$

Given- a and b are the zeroes of the quadratic polynomial

$kx^2+4x+4$

$a^2+b^2=24$

Find the value of k

Solution - In algebra, a quadratic equation is any equation that can be rearranged in standard form as $ax^{2}+bx+c=0$ where x represents an unknown, and a, b, and c represent known numbers, where $a \neq 0$. If a = 0, then the equation is linear, not quadratic, as there is no $ax^2$ term.

a, b roots of $f(x)=kx^2+4x+4$

$a^2+b^2=24$

we know $a+b=\frac{-b}{a} =\frac{-4}{k}$

$ab=\frac{c}{a}=\frac{4}{k}$

$(a+b)^2=a^2+b^2+2ab$

$(\frac{-4}{k} )^2=24+2\times \frac{4}{k}$

$\frac{16}{k^2}=24+\frac{8}{K}\Rightarrow 16=24k^2+8k$

$2=3k^2+k\\3k^2+k-2=0\\3k^2+3k-2k-2=0\\3k(k+1)-2(k+1)\\(k+1)(3k-2)\\k=-1,\frac{2}{3}$

Hence, the value of k is $-1, \frac{2}{3}$

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