find q quadratic polynomial the sum and the product of whose zeroes are -8 and 12 respectively. hence ,find the zeroes. please send the picture
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find q quadratic polynomial the sum and the product of whose zeroes are -8 and 12 respectively. hence ,find the zeroes. please send the picture
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Answer:
Answer: x²+2x–8
Let the assume quadratic polynomial be ax²+bx+c=0, where a≠0 and it’s zeroes be α and β.
Here
α = -4
β = 2
We know that
(1) Sum of the zeroes
⇒ α + β
⇒ -4 + 2
⇒ -2……………………………(1)
(2) Product of the zeroes
⇒ α × β
⇒ -4 × 2
⇒ -8……………………………(2)
∴ The quadratic polynomial ax²+bx+c is k[x2 + (α + β)x + αβ]
Where k is constant.
k[x2 + (α + β)x + αβ]
From equation (1) and (2) we get
⇒ k[x2 -2x -8]
When k = 1 the quadratic equation will become
x2 -2x -8