Question

The equation whose roots are smaller by 1 than those of 2x²-5x+6=0 is.

A) 2x² - 9x + 13 = 0

B) 2x² - x + 3 = 0

C) 2x² + 9x + 13 = 0

D) 2x² + x + 3 = 0

I want with Solution plz don't SPAM!​

Answer 1

Solution :-

Let us assume that, the roots of quadratic equation 2x² - 5x + 6 = 0 are p and q .

so,

→ sum of roots = (-b/a)

→ p + q = -(-5)/2

→ (p + q) = (5/2)

and,

→ Product of roots = c/a

→ p * q = 6/2

→ pq = 3 .

now, since roots of other equation are smaller by 1 . They will be (p - 1) and (q - 1) .

so,

→ sum of roots = (p - 1) + (q - 1) = (p + q) - 2 = (5/2) - 2 = (1/2)

and,

→ product of roots = (p - 1) * (q - 1) = pq - p - q + 1 = pq - (p + q) + 1 = 3 - (5/2) + 1 = 4 - (5/2) = (3/2)

therefore, Required quadratic equation will be,

→ x² - sum of roots * x + product of roots = 0

→ x² - (1/2)x + (3/2) = 0

→ (2x² - x + 3)/2 = 0

→ 2x² - x + 3 = 0 (B) (Ans.)

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