Question

1)
If the ratio of the roots of the quadratic equation ax2 + cx + c = 0 is p:q, then prove that√p/q+√q/p+√c/a=0​

Answer 1

√p/q+√q/p+√c/a=0​ if the ratio of the roots of the quadratic equation ax² + cx  + c = 0 is p:q

Step-by-step explanation:

ax² + cx  + c = 0

Let  say roots are

α & β

Then α/β = p/q

α + β = - c/a

αβ = c/a

√p/q+√q/p+√c/a=0​

LHS = √p/q+√q/p+√c/a

= √α/β+√β/α+√c/a

= (α + β)/√αβ  + √c/a

= (- c/a)/√c/a + √c/a

= - √c/a + √c/a

= 0

= RHS

QED

Proved

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