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# If Sin α and Cos α Are the Roots of the Equations Ax2 + Bx + C = 0, Then B2 = - CBSE Class 10 - Mathematics

ConceptSolutions of Quadratic Equations by Factorization

#### Question

If sin α and cos α are the roots of the equations ax2 + bx + c = 0, then b2 =

•  a2 − 2ac

•  a2 + 2ac

• a2 − ac

• a2 + ac

#### Solution

The given quadric equation is ax^2 + bx + c = 0, and sin alpha and cos beta are roots of given equation.

And, a = a,b = b and, c = c

Then, as we know that sum of the roots

sin alpha + cos beta - (-b)/a…. (1)

And the product of the roots

sin alpha .cos beta =c/a…. (2)

Squaring both sides of equation (1) we get

(sin alpha + cos beta)^2 = ((-b)/a)^2

sin^2 alpha + cos^2 beta + 2 sin alpha cos beta = b^2/a^2

Putting the value of sin^2 alpha + cos^2 beta = 1, we get

1 + 2 sin alpha cos beta = b^2/a^2

a^2 (1+2 sin alpha cos beta) = b^2

Putting the value ofsin alpha.cos beta = c/a , we get

a^2 (1 + 2 c/a) = b^2

a^2 ((a+2c)/a) = b^2

a^2 + 2ac =b^2

Therefore, the value of b^2 = a^2 + 2ac.

Is there an error in this question or solution?

#### APPEARS IN

Solution If Sin α and Cos α Are the Roots of the Equations Ax2 + Bx + C = 0, Then B2 = Concept: Solutions of Quadratic Equations by Factorization.
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