Question

if a anb B are zero's of quadratic polynomial p(x) = x²- 8x + k ,such that a-B = 4 ,then value of k is
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Answer 1

Answer:

Given:−

p(x) = x² - 8x + k

α² + β² = 40

\large\bf\underline {To \: find:-}Tofind:−

Value of k.

\huge\bf\underline{Solution:-}Solution:−

it is given that α and β are the zeroes of the given polynomial.

»»p(x) = x² - 8x + k

a = 1

b = -8

c = k

≫ Sum of zeroes = - b/a

⠀⠀⠀⠀⠀»» α + β = -(-8)/1

⠀⠀⠀⠀⠀»» α + β = 8

≫ product of zeroes = c/a

⠀⠀⠀⠀⠀»» αβ = k

we know that,

★ (a + b) ² = a² + b² + 2ab

≫ (a + b)² - 2ab = a² + b²

So,

⠀⠀⠀⠀⠀»» (α + β)² - 2ab = a² + b²

⠀⠀⠀⠀⠀»» 8² -2× k = 40

⠀⠀⠀⠀⠀»» 64 - 2k = 40

⠀⠀⠀⠀⠀»» - 2k = 40 - 64

⠀⠀⠀⠀⠀»» - 2k = -24

⠀⠀⠀⠀⠀»» k = -24/-2

⠀⠀⠀⠀⠀»» k = 12

✦ Value of k is 12.