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# 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.
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