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Find the Values Of K For Which the Roots Are Real and Equal in Each of the Following Equation: - CBSE Class 10 - Mathematics

ConceptSolutions of Quadratic Equations by Factorization

Question

Find the values of k for which the roots are real and equal in each of the following equation:$px(x - 3) + 9 = 0$

Solution

The given quadratic equation is  $px(x - 3) + 9 = 0$ and roots are real and equal.

Then find the value of p.

Here,

$px(x - 3) + 9 = 0$

$\Rightarrow p x^2 - 3px + 9 = 0$

So,

$a = p, b = - 3p \text { and } c = 9 .$

As we know that $D = b^2 - 4ac$

Putting the value of $a = p, b = - 3p \text { and } c = 9 .$

$D = \left( - 3p \right)^2 - 4\left( p \right)\left( 9 \right)$

$= 9 p^2 - 36p$

The given equation will have real and equal roots, if D = 0.

So,

$9 p^2 - 36p = 0$

Now factorizing the above equation,

$9 p^2 - 36p = 0$

$\Rightarrow 9p\left( p - 4 \right) = 0$

$\Rightarrow 9p = 0 \text { or } p - 4 = 0$

$\Rightarrow p = 0 \text { or } p = 4$

Therefore, the value of $p = 0, 4 .$

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Solution Find the Values Of K For Which the Roots Are Real and Equal in Each of the Following Equation: Concept: Solutions of Quadratic Equations by Factorization.
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