Question

Find a quadratic equation in X whose roots are -2 and 3/4​

Answer 1

The quadratic formula states that the roots of the equation ax^2 + bx + c = 0 are given by (-b ± √(b^2 - 4ac))/(2a). To find a quadratic equation whose roots are -2 and 3/4, we can set these values equal to (-b ± √(b^2 - 4ac))/(2a) and solve for the values of a, b, and c.

One such equation is (x+2)(x-3/4) = 0. Expanding this product, we get x^2 - x/2 + 3/8 = 0

Another equation is x^2 - 4x + 8 = 0 (by Vieta's Formulas)

Answer 2

4x² + 5x - 6 = 0

Explanation:

Quadratic equation:

`\boxed{x^2-(sum \ of \ roots)x+product \ of \ roots=0}`

`Sum \ of \ roots = -2 + (3)/(4)`

`= (-2*4)/(1*4)+(3)/(4)\\\\=(-8)/(4)+(3)/(4)\\\\=(-5)/(4)\\\\`

`\sf product \ of \ roots =-2 *(3)/(4)`

`=(-6)/(4)`

Quadratic equation:

`x^2 - \left((-5)/(4)\right)x+\left((-6)/(4)\right)=0`

Multiply the entire equation by 4,

4x² - (-5)x + (-6) = 0

4x² + 5x - 6 = 0