Question

(b) If the ratio of the roots of the quadratic equation x² - px + q = 0 be a : b, then prove that
p’ab = q (a + b)2​

Answer 1

Step-by-step explanation:

: As stated, the theorem isn’t true. A similar but truer statement is,

Given real non-zero p,q, let a,b be the roots of px2+qx+q=0. Then,

qp=ba+ab+2

Answer 2

Step-by-step explanation:

lets assume the roots are ax and bx

As we know

ax+bx= -p

or, x(a+b)=-p

or, x= -p/a+b .......... eq.1

we know also

ax*bx=q

or, x^2ab=q

or, x^2=q/ab

or, (-p/a+b)^2=q/ab ...by putting the value of x from eq.1

or, p^2/(a+b)^2=q/ab

or, p^2ab=q(a+b)^2 ...... proved