The equation that has only one real number solution is
4a²x²+4abx+ b² = 0 and the solution is x = -b/2a where a, b, and c are real values.
What is a quadratic equation?
Any equation of the form [tex]\rm ax^2+bx+c=0[/tex] Where x is variable and a, b, and c are any real numbers where a ≠ 0 is called a quadratic equation.
As we know, the formula for the roots of the quadratic equation is given by:
[tex]\rm x = \dfrac{-b \pm\sqrt{b^2-4ac}}{2a}[/tex]
If the quadratic equation has only one solution, then
[tex]\rm b^2 - 4ac = 0[/tex] or
[tex]\rm b^2 = 4ac[/tex]
[tex]\rm x = \dfrac{-b}{2a}[/tex]
2ax = - b
(2ax+b) = 0
(2ax+b)² = 0 (square on both sides)
[tex]\rm 4a^2x^2 + 4abx+ b^2 = 0[/tex]
Thus, the equation that has only one real number solution is
4a²x²+4abx+ b² = 0 and the solution is x = -b/2a where a, b, and c are real values.
Learn more about quadratic equations here:
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