CBSE Class 10 Math Question Paper 2016 | Q5

CBSE Maths Board Paper Solution | 2 Mark Question | Quadratic Equation: Equal roots

Question 5: If -5 is a root of the quadratic equation 2x2 + Px - 15 = 0 and the quadratic equation P(x2 + x) + K = 0 has equal roots, find the value of K.

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Explanatory Answer | CBSE 2016 Maths Board Paper Q5

Step 1: Find P

-5 is a root of 2x2 + Px - 15 = 0
Because -5 is a root of the equation, substituting x = -5 in the equation will satisfy the equation.
Substitute x = -5 in the equation to find P.
2(-5)2 + P(-5) - 15 = 0
50 - 5P - 15 = 0
5P = 35 or P = 7

Step 2: Find K

The equation P(x2 + x) + K = 0 has equal roots.
i.e., 7x2 + 7x + K = 0 has equal roots
If a quadratic equation ax2 + bx + c = 0 has real and equal roots, its discriminant, b2 - 4ac = 0
i.e., 72 - 4 × 7 × K = 0
28K = 49 or K = $\frac{49}{28}$ = $\frac{7}{4}$

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