Page 9 - 10-Math-1 QUADRATIC EQUATIONS

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EXERCISE 1.2

1. Solve the following equations using quadratic formula:

(i) 2 - x2 = 7x (ii) 5x2 + 8x + 1 = 0

1.4 Equations reducible to quadratic form Version 1.1

We now discuss different types of equations, which can be reduced
to a quadratic equation by some proper substitution.

Type (i) The equations of the type ax4 + bx2 + c = 0
Replacing x2 = y in equation ax4 + bx2 + c = 0, we get a quadratic
equation in y.

Example 1: Solve the equation x4 - 13x2 + 36 = 0.

Solution: x4 - 13x2 + 36 = 0
Let x2 = y. Then x4 = y2
Equation (i) becomes
y2 - 13y + 36 = 0 which can be factorized as
y2 - 9y - 4y + 36 = 0
y(y - 9) - 4(y - 9) = 0
(y - 9) (y - 4) = 0
Either y - 9 = 0 or y - 4 = 0 , that is,
y = 9 or y = 4
Put y = x2
x2 = 9 or x2 = 4
⇒ x = + 3 or x = +2
∴ The solution set is { +2, +3 }

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