Share

Write the Condition to Be Satisfied for Which Equations Ax2 + 2bx + C = 0 and B X 2 − 2 √ a C X + B = 0 Have Equal Roots. - CBSE Class 10 - Mathematics

ConceptSolutions of Quadratic Equations by Factorization

Question

Write the condition to be satisfied for which equations ax2 + 2bx + c = 0 and $b x^2 - 2\sqrt{ac}x + b = 0$ have equal roots.

Solution

The given equations are

ax2 + 2bx + c = 0  …... (1)

And, $b x^2 - 2\sqrt{ac}x + b = 0$ …… (2)

roots are equal.

Let D1 and D2 be the discriminants of equation (1) and (2) respectively,

Then,

D1 = (2b)^2 - 4ac

= 4b^2 - 4ac

And  D_= (-2sqrtac)^2 - 4 xx b xx b

 = 4ac - 4b^2

Both the given equation will have real roots, if  D_1 ≥0 " and " D_2 ≥ 0

4b^2 - 4ac ≥ 0

4b^2 ≥ 4ac

b^2 ≥ ac…… (3)

4ac - 4b^2 ≥ 0

  4ac ≥ 4b^2

ac ≥ b^2 …... (4)

From equations (3) and (4) we get

b2 = ac

Hence, b2 = ac is the condition under which the given equations have equal roots.

Is there an error in this question or solution?

APPEARS IN

Solution Write the Condition to Be Satisfied for Which Equations Ax2 + 2bx + C = 0 and B X 2 − 2 √ a C X + B = 0 Have Equal Roots. Concept: Solutions of Quadratic Equations by Factorization.
S