Answer the following and justify:Can the quadratic polynomial $x^{2}+k x+k$ have equal zeroes for some odd integer $k>1$ ?

AcademicMathematicsNCERTClass 10

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Given:

Quadratic polynomial $x^{2}+k x+k$ and $k>1$.

To do:

We have to find whether the quadratic polynomial $x^{2}+k x+k$ can have equal zeroes for some odd integer $k>1$.

Solution:

Let $p(x) = x^2 + kx + k$

If $p(x)$ has equal zeroes, then its discriminant is zero.

$D = b^2 -4ac = 0$                        Here,

$a =1, b = k$ and $c = k$

Therefore,

$(k)^2-4(1)(k) = 0$

$k(k- 4)=0$

$k =0$ or $k=4$

This implies, the quadratic polynomial $p(x)$ has equal zeroes at $k =0, 4$.

Hence, the quadratic polynomial $x^{2}+k x+k$ cannot have equal zeroes for some odd integer $k>1$.

Updated on 10-Oct-2022 13:27:09

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