RS Aggarwal - Mathematics

Book: RS Aggarwal - Mathematics

Chapter: 10. Quadratic Equations

Subject: Maths - Class 10th

Q. No. 22 of Exercise 10D

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22

If the roots of the equations ax2 + 2bx + c = 0 and are simultaneously real then prove that b2 = ac.

Given the roots of the equations ax2 + 2bx + c = 0 are real.

Comparing with standard quadratic equation Ax2 + Bx + C = 0


A = a B = 2b C = c


Discriminant D1 = B2 – 4AC ≥ 0


= (2b)2 – 4.a.c ≥ 0


= 4(b2 –ac) ≥ 0


= (b2 –ac) ≥ 0 – – – – – (1)


For the equation


Discriminant D2 = b2 – 4ac ≥ 0


=


= 4(ac – b2) ≥0


= – 4(b2–ac) ≥0


= (b2 –ac) ≥0 – – – – – (2)


The roots of the are simultaneously real if (1) and (2) are true together


b2 –ac = 0


b2 = ac


Hence proved.


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