Question

Determine the quadratic equation, whose Sum and Product of roots are -3/2 and -1 ​

Answer 1

Answer:

If the roots are given, general form of the quadratic equation is x – (sum of the roots) x2 + product of the roots = 0. (i) Sum of the roots = -9 Product of the roots = 20 The equation = x2 – (-9x) + 20 = 0 ⇒ x2 + 9x + 20 = 0 (ii) Sum of the roots = 5/3 Product of the roots = 4 Required equation = x2 – (sum of the roots)x + product of the roots = 0 ⇒ x2 – (5/3)x + 4 = 0 ⇒ 3x2 – 5x + 12 = 0 (iii) Sum of the roots = (-3/2) (α + β) = -3/2 Product of the roots (αβ) = (-1) Required equation = x2 – (α + β)x + αβ = 0 x2 – (-3/2)x – 1 = 0 2x2 + 3x – 2 = 0 (iv) α + β = – (2 – a)2 αβ = (a + 5)2 Required equation = x2 – (α + β)x – αβ = 0 ⇒ x2 – (-(2 – a)2)x + (a + 5)2 = 0 ⇒ x2 + (2 – a)2 x + (a + 5)2 = 0

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Answer 2

Answer:

the roots are given, general form of the quadratic equation is x – (sum of the roots) x2 + product of the roots = 0. (i) Sum of the roots = -9 Product of the roots = 20 The equation = x2 – (-9x) + 20 = 0 ⇒ x2 + 9x + 20 = 0 (ii) Sum of the roots = 5/3 Product of the roots = 4 Required equation = x2 – (sum of the roots)x + product of the roots = 0 ⇒ x2 – (5/3)x + 4 = 0 ⇒ 3x2 – 5x + 12 = 0 (iii) Sum of the roots = (-3/2) (α + β) = -3/2 Product of the roots (αβ) = (-1) Required equation = x2 – (α + β)x + αβ = 0 x2 – (-3/2)x – 1 = 0 2x2 + 3x – 2 = 0 (iv) α + β = – (2 – a)2 αβ = (a + 5)2 Required equation = x2 – (α + β)x – αβ = 0 ⇒ x2 – (-(2 – a)2)x + (a + 5)2 = 0 ⇒ x2 + (2 – a)2 x + (a + 5)2 = 0-