Question

If one root of ax^2 + bx+ c= 0 is double the other, then prove that 2b^2 = 9ac

Answer 1

If  α and β are the roots of Quadratic Equation ax² + bx + c = 0 then :

Sum of the roots : α + β = -b/a

Product of the roots : α × β = c/a

Given that one root is double the other

⇒ We can assume that α = 2β

⇒ Sum of the roots : 2β + β = -b/a

⇒ 3β = -b/a

⇒ β = -b/3a

Product of the roots : 2β × β = c/a

⇒ 2β² = c/a

⇒ β² = c/2a

But we found that β = -b/3a

⇒ (-b/3a)² = c/2a

⇒ b²/9a² = c/2a

⇒ b²/9a = c/2

⇒ 2b² = 9ac

Answer 2

Step-by-step explanation:

YO YO YO .........HOPE IT WILL HELP U