Question

The sum and the product of the
zeroes of a quadratic polynomial are
-1/2 and 12 respectively, then the
polynomial is
a. 2x²+x+1
b. 2x²-x+1
c. 2x²-x-1
d. 2x²+x-1
ans fast
​

Answer 1

$\huge{\underline{\bf{\blue{Question:-}}}}$

The sum and the product of the zeroes of a quadratic polynomial are-1/2 and 12 respectively, then the polynomial is ..

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$\large{\underline{\bf{\pink{Answer:-}}}}$

the quadratic polynomial is ⠀⠀⠀⠀⠀⠀⠀2x² - x +24 = 0

$\large{\underline{\bf{\purple{Explanation:-}}}}$

$\large{\underline{\bf{\green{Given:-}}}}$

✰ sum of zeroes = -1/2

✰ product of zeroes = 12

$\large{\underline{\bf{\green{To\:Find:-}}}}$

✰ we need to find the polynomial.

$\huge{\underline{\bf{\red{Solution:-}}}}$

Let α and β are the zeroes of required polynomial f(x).

Then,

➜ (α + β) = -1/2

➜ and ( αβ ) = 12

∴ f(x) = x² +(α + β) x + ( αβ )

⠀⠀⠀⠀⠀

➩ ⠀= x² + (-1/2)x + 12

➩ ⠀= x² - x/2 + 12

➩ ⠀(2x² - x +24)/2 = 0

➩⠀⠀ 2x² - x +24 = 0 × 2

➥⠀⠀⠀⠀⠀⠀2x² - x +24 = 0

Hence the quadratic polynomial is

⠀⠀⠀⠀⠀⠀⠀2x² - x +24 = 0

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