Construct a quadratic equation with roots 7 and -3.

1.	Construct a quadratic equation with roots 7 and -3.
Answer» The given roots are 7 and -3 Let α = 7 and β = -3 α + β = 7 – 3 = 4 αβ = (7)(-3) = -21 The quadratic equation with roots α and β is x² – (α + β) x + αβ = 0 So the required quadratic equation is x² – (4) x + (-21) = 0 (i.e.,) x² – 4x – 21 = 0

Answer»

The given roots are 7 and -3

Let α = 7 and β = -3

α + β = 7 – 3 = 4

αβ = (7)(-3) = -21

The quadratic equation with roots α and β is x² – (α + β) x + αβ = 0

So the required quadratic equation is

x² – (4) x + (-21) = 0

(i.e.,) x² – 4x – 21 = 0

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