Question

check whether(2x-1)(x-3)=(x+5)(x-1) is a quadratic equations or not by simplifying​

Answer 1

Required Answer:-

It is a quadratic equation.

Solution:-

A quadratic equation has the highest degree of 2. Let's simplify the equation first.

Given Equation:-

Simplify the terms.

$\rightarrow (2x-1)(x-3)=(x+5)(x-1)$

$\rightarrow 2x^2-6x-x+3=x^2-x+5x-5$

$\rightarrow 2x^2-7x+3=x^2+4x-5$

Collect like terms.

$\rightarrow (2-1)x^2+(-7-4)x+3+5=0$

$\rightarrow x^2-13x+8=0$

This equation has the highest power of 2, which coefficient is nonzero. So, we can say this is a quadratic equation.

Learn more:-

There are three ways to solve a quadratic equation:-

• Factoring
• Complete the Square
• Quadratic Formula

→ Factoring uses the logic that the product of any number and zero is zero. Complete the square method uses square root, and the quadratic formula is the simpler method of it.

Quadratic Formula $x=\dfrac{-b\pm\sqrt{b^2-4ac} }{2a}$