Question

If one root of the equation px²+qx+r=0 is four times the other, show that 4q²-25pr=0​

Answer 1

Proved.

Explanation:

Quadratic equation:

px² + qx + r = 0

α = 4β

`\sf \alpha + \beta =(-b)/(a)\\\\ 4\beta +\beta =(-q)/(p)\\\\`

`\sf 5\beta =(-p)/(q)\\\\\beta =(-p)/(5q)-------(I)\\\\\alpha * \beta = (c)/(a)\\\\4\beta *\beta =(q)/(r)\\\\ 4\beta^2=(q)/(r)`

`\sf4 *((-q)/(5p))^2=(r)/(p)\\\\\\ 4(q^2)/(25p^2)=(r)/(p)\\\\4q^2=(r)/(p)*25p^2\\\\`

4q² = 25rp

4q² - 25pr = 0