Question

Let us Express 3xsquare + 7x + 23 = (x+4) (x+3) +2 in the form of the quadratic equation ax(square)+bx+c = 0 (a=0)​

Answer 1

We are asked to express 3x² + 7x + 23 = (x + 4)(x + 3) + 2 in the form of a quadratic equation:

A quadratic equation is the form of ax² + bx + c = 0.

a = Coefficient of x².

b = Coefficient of x.

c = Constant term.

⇔ 3x² + 7x + 23 = (x + 4)(x + 3) + 2

⇔ 3x² + 7x + 23 = x(x + 3) + 4(x + 3) + 2

⇔ 3x² + 7x + 23 = x² + 3x + 4x + 12 + 2

⇔ 3x² + 7x + 23 - x² - 3x - 4x - 12 - 2 = 0

⇔ 2x² + 7x + 23 - 7x - 14 = 0

⇔ 2x² + 9 = 0

But this equation is not of the form ax² + bx + c = 0. Hence it can't be expressed as a quadratic equation.

Answer 2

★Answer:–

⭐ Quadratic equations ⭐

Standard Form

The Standard Form of a Quadratic Equation looks like this:

Quadratic Equation: ax^2 + bx + c = 0

a, b and c are known values. a can't be 0.(a≠0)

"x" is the variable or unknown (we don't know it yet).

★Solution:–

$\implies \: {3x}^{2} + 7x + 23 = (x + 4)(x + 3) + 2$

$\implies {3x}^{2} + 7x + 23 = x(x + 4) + 3( + 4) + 2$

$\implies {3x}^{2} + 7x + 23 = {x}^{2} + 4x + 3x + 12 + 2$

$\implies {3x}^{2} + 7x + 23 = {x}^{2} + 7x + 14$

$\implies {3x}^{2} + 7x + 23 = {x}^{2} + 7x + 14$

$\implies {3x}^{2} + 7x + 23 - {x}^{2} + 7x + 14 = 0$

$\implies {3x}^{2} - {x}^{2} + 7x - 7x + 23 + 14 = 0$

$\implies {2x}^{2} + 9 = 0$

therefore,

It is not in the form of quadratic equations.So, it is not a Quadratic equations.