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# If P and Q Are the Roots of the Equation X2 − Px + Q = 0, Then - Mathematics

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#### Question

If p and q are the roots of the equation x2 − px + q = 0, then

##### Options
• p = 1, q = −2

• p = 1, q = −2

• p = −2, q = 0

• p = −2, q = 1

#### Solution

Given that p and be the roots of the equation  x2 − px + q = 0

Then find the value of p and q.

Here, a = 1,b= -p and,c = q

p and q be the roots of the given equation

Therefore, sum of the roots

p+q = (-b)/ a

=(-p)/1

=-p

q = -p -p

= -2p….. (1)

Product of the roots

As we know that

p xx q = q/1

p = q/q

= 1

Putting the value of p=1 in equation (1)

q = -2 xx 1

= -2

Therefore, the value of  p = 1 ; q = -2 .

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#### APPEARS IN

RD Sharma Solution for Class 10 Maths (2018 (Latest))
Chapter 4: Quadratic Equations
Q: 13 | Page no. 83
RD Sharma Solution for Class 10 Maths (2018 (Latest))
Chapter 4: Quadratic Equations
Q: 13 | Page no. 83
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If P and Q Are the Roots of the Equation X2 − Px + Q = 0, Then Concept: Solutions of Quadratic Equations by Factorization.
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