Question

check whether (x-2)(x+5) = (x-3)(x+4) + x² is a quadratic equation​

Answer 1

Answer:

Yes, (x - 2)(x + 5) = (x - 3)(x + 4) + x² is a quadratic equation.

Step-by-step explanation:

For an equation to be quadratic, it has to be of the form ax² + bx + c.

⇒ (x - 2)(x + 5) = (x - 3)(x + 4) + x²

⇒ x² + 5x - 2x - 10 = x² + 4x - 3x - 12 + x²

⇒ x² + 3x - 10 = 2x² + x - 12

⇒ x² - 2x² + 3x - x - 10 + 12 = 0

⇒ -x² + 2x + 2 = 0

The above equation is of the form ax² + bx + c where;

a → -1

b → 2

c → 2

Hence, this is a quadratic equation.

Answer 2

Step-by-step explanation:

ǫᴜᴀᴅʀᴀᴛɪᴄ ᴇǫᴜᴀᴛɪᴏɴ:

The quadratic formula helps us solve any quadratic equation. First, we bring the equation to the form ax²+bx+c=0, where a, b, and c are coefficients.

ᴀᴄᴄᴏʀᴅɪɴɢ ᴛᴏ ǫᴜᴇsᴛɪᴏɴ:

$(x - 2)(x + 5) = (x - 3)(x + 4) + {x}^{2}$

${x}^{2} - 2x + 5x - 10 = {x}^{2} - 3x + 4x - 12 + {x}^{2}$

${x}^{2} + 3x - 10 = 2 {x}^{2} + x - 12$

${x}^{2} + 3x - 10 - 2 {x}^{2} - x + 12 = 0$

$- {x}^{2} + 2x + 2 = 0$

it is in the form of quadratic equation.