Question

What are two numbers that can add to 7 but multiply to -30

Answer 1

Answer:

The two numbers that can add to 7 but multiply to -30 are $X=10 , Y=-3$

Step-by-step explanation:

• A quadratic equation can be represented as

                                     $ax^{2} +bx+c=0$

• The roots of such an equation can be calculated by using the formula

                    $x=\frac{-b+\sqrt{b^{2}-4ac } }{2a}$    or $x=\frac{-b-\sqrt{b^{2}-4ac } }{2a}$

From the question, we have

two numbers added to $7$ and multiplied to $-30$

let the numbers be  X and Y

⇒

$X+Y=7\\XY=-30\\X=-30/Y$

substitute the value of X in the above equation

⇒

$\frac{-30}{Y}+Y=7\\-30+Y^{2}=7Y\\Y^{2}-7Y-30=0$

by rearranging the equation we got a quadratic equation with coefficients

$a=1\\b=-7\\c=-30$

now the roots are

$x=\frac{7+\sqrt{7^{2}-4*1*-30 } }{2}=10$   or $x=\frac{7-\sqrt{7^{2}-4*1*-30 } }{2}=-6$

when $x=10$

$10+Y=7\\Y=-3$

so the numbers are $X=10 , Y=-3$

(For $x=-6$ it is not valid )