Question

If roots of the equation ax² + 2bx + c = 0 and bx² - 2 (ac) ½ × +b =0 are simultaneously real then prove that be =ac​

Answer 1

Let D 1and D2

be the discriminants of the two equations, then

D1≥0 and D2≥0

⇒4b2−4ac ≥0 and 4ac−4b2 ≥0

⇒b2≥ac and ac≥b2

⇒b2 =ac

here b2=(b)2

means b whole power 2

(or)

b whole square