Question

find value of k if α and β are the zeros of the polynomial x²-8x+k such that α²+β²=40
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Answer 1

Answer:

k=12

(a+b) ²-2ab=a²+b²

64-40=2ab

24=2ab

ab=12

k=12

Answer 2

EXPLANATION.

→ if a and b are the zeroes of the polynomial

x² - 8x + k.

→ such that = a² + b² = 40.

→ To find the value of k.

→ sum of zeroes of quadratic polynomial.

a + b = -b/a

a + b = 8 ......(1)

→ products of zeroes of quadratic polynomial.

ab = c/a

ab = k .......(2)

→ a² + b² = 40

→ Formula of ( a² + b²) = ( a + b)² - 2ab.

→ ( a + b)² - 2ab = 40

→ ( 8)² - 2(k) = 40

→ 64 - 2k = 40

→ - 2k = 40 - 64

→ - 2k = -24

→ k = 12

→ value of k = 12.