Question

Verify that 2,-1,-1/2 are the zeros of the polynomial2Xsquare+X-1

Answer 1

Question :-

Verify that 2, -1 and -1/2 are the zeros of the polynomial 2x² + x - 1

Answer :-

→ only -1 is a zero of the given polynomial in the given numbers .

Explanation :-

If we need to verify zeros of any Quadratic the put value of zeros in that polynomial if this will equal to zero then we can say that is the zero is that polynomial ,

Let ,f(x) = 2x² + x - 1

According to the question,

Firstly when we take 2 ,

then we will have to appear that f(2) = 0

→ f(2) = 2× 2² + 2 - 1

→ f (2) = 9 ≠0

it means 2 is not a zeros of the given polynomial.

now we take -1 ,

hence,

→ f(-1) = 2× (-1)² + (-1) -1

→ f(-1) = 2 -2 = 0

therefore -1 is a root of the given polynomial.

now we take -1/2

therefore ,

→ f(-1/2) = 2 × (-1/2)² -1/2 -1

→ f(-1/2) = 1/2 -1/2 -1 ≠ 0

hence we can say that -1/2 is not a zeros of the given polynomial .

Only -1 is the zeros of this given polynomial in the given numbers .

Hence verified.

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