Class 10 Math All topics Quadratic Equations

Find a quadratic polynomial with zeros at $x=41 $ and $x=−1.$

Solution: Let $α$ and $β$ be the zeros of p(x) Using the relationship between zeros and coefficients, we have

$p(x)=x_{2}−(α+β)x+αβ$

$=x_{2}−(41 −1)x+(41 )(−1)$

$=x_{2}+43 x−41 $

It is a polynomial with zeros $41 $ and $−1$.

Aliter : The required polynomial is obtained directly as follows:

$p(x)=(x−41 )(x+1)$

$=x_{2}+43 x−41 $

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

$p(x)=x_{2}−(α+β)x+αβ$

$=x_{2}−(41 −1)x+(41 )(−1)$

$=x_{2}+43 x−41 $

It is a polynomial with zeros $41 $ and $−1$.

Aliter : The required polynomial is obtained directly as follows:

$p(x)=(x−41 )(x+1)$

$=x_{2}+43 x−41 $

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

Similar topics

introduction to trigonometry

functions

some applications of trigonometry

quadratic equations

polynomials

introduction to trigonometry

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quadratic equations

polynomials

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