In algebra, a quadratic equation can be written in the form:
ax2 + bx + c = 0
where x is the variable and a, b, c are the real numbers and a≠0. If a=0 then it will be a linear equation not quadratic because no second order term.
If quadratic equation has solution then it can be found by using the quadratic formula.
- Example-1: Solve the quadratic equation for x,
x2 + 10x -24 = 0
Solution: In the quadratic equation, we have,
a=1, b=10 and c=-24
Therefore the quadratic formula yields
Hence, two solutions for the above equations are:
x = 4/2 = 2, And x = -24/2 = -12
- Example-2: Solve the quadratic equation using factorization,
x2 + 2x - 15 = 0
Solution: Given equation,
x2 + 2x - 15 = 0
It can be factorize as,
x2 -3x + 5x - 15 = 0 x(x - 3) + 5(x - 3) = 0 (x - 3)(x + 5) = 0
Hence, two solutions for x are:
x = 3 and x = -5
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