Question

If one root of the equation x2+7x +m =0exceeds the other by unity . then find m.

Answer 1

Answer:

12

Step-by-step explanation:

As one exceeds the other by unity, let the roots be p ans p+1

Sum of roots = p + p + 1 = 2p + 1 = -7    (-b/a)

2p = -8  => p = -4

Product of roots = m (c/a) = p*(p + 1) = -4*-3 = 12.

∴ m = 12

Answer 2

GIVEN :–

• One root of the equation x² + 7x + m = 0 exceeds the other by unity.

TO FIND :–

• Value of 'm' = ?

SOLUTION :–

• Let the first root of quadratic equation x² + 7x + m = 0 is α then second root is α + 1 .

• We know that –

✯ Sum of roots = -(coffieciant of x)/(coefficient of x²)

⇒ (α) + (α + 1) = -(7)/(1)

⇒ α + α + 1 = -7

⇒ 2α = -7 - 1

⇒ 2α = -8

⇒ α = -(8/2)

⇒ α = -4

• We also know that –

✯ Product of roots = -(constant term)/(coefficient of x²)

⇒ (α).(α + 1) = (m)/(1)

⇒ (-4)(-4 + 1) = m

⇒ (-4)(-3) = m

⇒ m = 12

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