One of the roots of the equation 5x^2−36x+t=0 is five times as big as the other root. find the value of t.

t = 36

Step-by-step explanation:

If you divide the equation by 5, you have ...

... x^2 -7.2x +t/5 = 0

The opposite of the sum of the roots is the coefficient of the linear term, so is 7.2. If the roots are "r" and "5r", then their sum is r+5r = 6r, so the value of r is ...

... 7.2/6 = 1.2

The roots are 1.2 and 5·1.2 = 6.

The constant term t/5 is the product of the roots, so ...

... t/5 = 1.2 · 6

... t = 6·6 = 36 . . . . . multiply by 5

`1234567890-=/*-qwertyuiop[]asdfghjkl; '\\zxcvbnm,./+ /