verify (2x+1)(3x+2)=6(x-1)(x-2) is a quadratic equation or not?explain
Answers
EXPLANATION.
Equation.
⇒ (2x + 1)(3x + 2) = 6(x - 1)(x - 2).
As we know that,
Expand this equation, we get.
⇒ 2x(3x + 2) + 1(3x + 2) = 6[x(x - 2) - 1(x - 2)].
⇒ 6x² + 4x + 3x + 2 = 6[x² - 2x - (x - 2)].
⇒ 6x² + 7x + 2 = 6[x² - 2x - x + 2].
⇒ 6x² + 7x + 2 = 6[x² - 3x + 2].
⇒ 6x² + 7x + 2 = 6x² - 18x + 12.
⇒ 6x² + 7x + 2 - 6x² + 18x - 12 = 0.
⇒ 7x + 18x + 2 - 12 = 0.
⇒ 25x - 10 = 0.
As we can see that,
Quadratic equation is in the form of = ax² + bx + c = 0 (a ≠ 0).
This equation is not a quadratic equation.
MORE INFORMATION.
Quadratic expression.
A polynomial of degree two of the form ax² + bx + c (a ≠ 0) is called a quadratic expression in x.
The quadratic equation.
ax² + bx + c = 0 (a ≠ 0) has two roots, given by.
⇒ α = - b + √D/2a.
⇒ β = - b - √D/2a.
D = Discriminant or b² - 4ac.
As, this equation doesn't have the degree as 2 or the biggest power of the variable as 2. it is not a quadratic equation.
done :D