Question

If alpha , beta are the zeros of the quadratic polynomial f(x) = kx + 4x + 4 such that alpha square +beta square =24 find the value 'k'.
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Answer 1

Answer:

The value of K= -1, 2/3

Step by Step...

a, b are roots of (x)= kx² +4x+4

Given=a²+b²=24

We known that a+b=-b/a=-4/k

ab=c/a=4/k

(a+b)²=a²+b²+2ab

(-4/k)²=24+2(4/k)

4²/k²=24+2(4/k)

16=24k²+8k

2=3k²+k

0=3k²+k-2

0=3k²+(3k-2k)-2

0=3k(k+1)-2(k+1)

0=(k+1)(3k-2)

k=-1 , 2/3

Answer 2

$\huge\fbox\red{αη}\fbox\green{s}\fbox\pink{ωε}\fbox\purple{я}$

a,β roots of f(x)= kx²+4x+4

Given,

a²+β²=24

${We\;know\;a+β\implies\frac{-b}{a}=\frac{-4}{k}}$

$\implies{aβ=\frac{c}{a}=\frac{4}{k}}$

$\implies{(aβ)²=a+²β²+2aβ}$

$\implies{(\frac{4}{k})²=24+2(\frac{4}{k})}$

$\implies{\frac{4²}{k²}=24+2\frac{4}{k}}$

16=24k²+8k

2=3k²+k

0=3k²+k-2

0=3k²+3k-2k-2

0=3k(k+1)-2(k+1)

0=(k+1)(3k-2)

Therefore,

$\downarrow\huge{\red{AnsweR}}$

$\huge{k=-1,\frac{2}{3}}$