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If One of the Equation Ax2 + Bx + C = 0 is Three Times Times the Other, Then B2 : Ac = - CBSE Class 10 - Mathematics

ConceptSolutions of Quadratic Equations by Factorization

Question

If one of the equation ax2 + bx + c = 0 is three times times the other, then b2 : ac =

• 3 : 1

• 3 : 16

• 16 : 3

• 16 : 1

Solution

Let alpha and betabe the roots of quadratic equationax^2 + bx + c = 0 in such a way that alpha = 3beta

Here, a = a, b = b and , c = c

Then,

according to question sum of the roots

alpha + beta = (-b)/a

3 beta + beta = (-b)/a

4beta = (-b)/a

alpha = (-b)/(4a)….. (1)

And the product of the roots

alpha . beta = c/a

3beta xx beta = c / a

3beta^2 = c/a

beta^2 = c /3a….. (2)

Putting the value of beta = (-b)/(4a) in equation (2)

(-b)/(4a)^2 = c /(3a)

(b^2)/(16a^2) = c/3a

b^2 = c/(3a) xx 16a^2

b^2 = (16ac)/3

b^2 / (ac) = 16/3

b^2 : ac = 16 :3

Is there an error in this question or solution?

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Solution If One of the Equation Ax2 + Bx + C = 0 is Three Times Times the Other, Then B2 : Ac = Concept: Solutions of Quadratic Equations by Factorization.
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