write the quadratic equation whose roots are 5and 1, and whose leading coefficient is 4

Question

write the quadratic equation whose roots are 5and 1, and whose leading coefficient is 4

Answer 1

A quadratic equation with roots of 5 and 1 may be expressed as:

(x - 5)(x - 1) = 0

Note: The multiplication property of zero states that if the product of two or more factors is zero, then at least one of the factors has to represent the number 0.

Using F-O-I-L,, this is x² - 6x + 5 = 0

Multiply by 4 to get: 4x² - 24x + 20 = 0

p.s., You may check this by using the quadratic formula.

Answer 2

Hi Keokia MayMay F.,

By now you probably know that the quadratic equation: ax^2 +bx +c = 0

has roots = (-b +- (b^2-4ac)^0.5)/2a .

and you are given that a =4

You should be able to work your way through to values for b and c from that?

Hint1: If you are clueless on how to proceed (I do hope not!), you might start by rearranging that equation for the roots into -b/2a +- (b^2-4ac)^0.5/2a . Then that +- split separates the given roots (5 and 1) -- but don't forget to work the 2a into your calculation

Hint2: since the 5 and 1 reflect the effect of the (+- term)/2a, therefore if you average them, you can solve for the -b/2a term alone.

Hope that gives you some ideas,

-- Cheers -- Mr. d.