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Find a quadratic polynomial with zeros at x={1}{4} and x = -1.

Question

Find a quadratic polynomial with zeros at $x = \frac{1}{4}$ and $x = - 1.$

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Liam Discussed

Find a quadratic polynomial with zeros at

x = \frac{1}{4}

and

x = - 1.

8 mins ago

Discuss this question LIVE

8 mins ago

Text solutionVerified

Let

α

and

β

be the zeros of p(x) Using the relationship between zeros and coefficients, we have

p (x) = x^{2} - (α + β) x + α β

= x^{2} - (\frac{1}{4} - 1) x + (\frac{1}{4}) (- 1)

= x^{2} + \frac{3}{4} x - \frac{1}{4}

It is a polynomial with zeros

\frac{1}{4}

and

- 1

.

Aliter : The required polynomial is obtained directly as follows:

p (x) = (x - \frac{1}{4}) (x + 1)

= x^{2} + \frac{3}{4} x - \frac{1}{4}

Any other polynomial with the desired property is obtained by multiplying p(x) by any nonzero real number.

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Question Text	Find a quadratic polynomial with zeros at $x = \frac{1}{4}$ and $x = - 1.$
Answer Type	Text solution:1
Upvotes	150