Question

Solve: 2 x ² - 16 x² +38x 24 =0, roots are
ratio.
in 3:4
​

Answer 1

Answer:

Let the roots of the given equation x3−12x2+39x−28=0 be a−d,a and a+d (Given that the roots are in A.P).

We know that the sum of the roots of a quadratic equation ax3+bx2+cx+d=0 is −ab and the product of the roots is ad.

Here, the equation is x3−12x2+39x−28=0, therefore, we have:

Sum of the roots is:

(a−d)+a+(a+d)=−1(−12)⇒3a=12⇒a=312⇒a=4

Product of the roots is:

(a−d)a(a+d)=28⇒(4−d)4(4+d)=28(Fromeqn(1))⇒(4−d)(4+d)=7⇒42−d2=7(∵x2−y2=(x+y)(x−y))⇒16−d