Question

If a ≠ 0 and a(l+m)² + 2blm + c = 0 and a(l+n)² +2bln+c= 0, then:
mn = l² + c/a
m+n = l² + bc/a
m + n = l² + c/a
mn = l² + bc/a​

Answer 1

Given :- a ≠ 0 and a(l+m)² + 2blm + c = 0 and a(l+n)² +2bln+c= 0, then:

A) mn = l² + c/a

B) m+n = l² + bc/a

C) m + n = l² + c/a

D) mn = l² + bc/a

Solution :-

given that,

→ a(l+m)² + 2blm + c = 0

→ a(l+n)² +2bln+c= 0

so, m and n both satisfy the equation :-

→ a(l + x)² + 2blx + c = 0

then, m ane n both are roots of the equation :-

→ a(l² + x² + 2lx) + 2blx + c = 0

→ al² + ax² + 2alx + 2blx + c = 0

→ ax² + 2alx + 2blx + al² + c = 0

→ ax² + (2al + 2bl)x + (al² + c) = 0

now, we know that, if roots of quadratic equation ax² + bx + c = 0 are p and q , then,

• p + q = (-b/a)
• p * q = c/a

therefore,

→ m * n = c/a

→ m * n = (al² + c)/a

→ m * n = (al²/a) + (c/a)

→ m * n = l² + (c/a) (A) (Ans.)

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