Question

Write the quadratic equation whose roots are
−4 and 6, and whose leading coefficient is 5.

Answer 1

You might begin with the general form of the quadratic equation, which is \[ax^2+bx+c=0\]

Answer 2

In terms of this equation, what can you say if you're told that -4 and 6 are roots of the equation and that the leading coefficient is 5?

Write this equation out, once for the root -4 and once for the root 6. These two equations provide you with enuf info to determine the values of the coefficients b and c.

Answer 3

so would it be 5x^2+20x-30=0?

Answer 4

You need to replace x by either -4 or 6.
This will eliminate x from the equation.
Yor goal is to find b and c.

If ax^2+bx+c=0, and x=-4, then 5(-4)^2+b(-4) +c=0.
Write a similar equation for the root x=6.
show your work.
simplify your results.
Solve your two resulting equations for b and c.

Answer 5

write*

Answer 6

Actually, you ARE trying to solve for b and c. Please follow my suggestions.

Answer 7

Coefficient a has the value 5 (given)
Find coefficients b and c.

Then write out your quadratic: y = ax^2 + bx + c.

Answer 8

\(y=a(x-b)(x-c)\) has leading coeficient \(a\) and roots \(b\) and \(c\).

Answer 9

ya'll makin this way to hard

Answer 10

imo

Answer 11

substitute -4 for x inside the first set of parentheses, and then subst. 6 for x inside the second set of parentheses. Use 5 as the coeff (a) of the highest ordered term (x^2).
Multiply out this whole expression and simplify it.

Now test x=-4 and x=6. If y our equation is correct, both of these x values should make the equation = 0. Show your work.