Advertisements
Advertisements
Question
Given that one root of the quadratic equation ax2 + bx + c = 0 is three times the other, show that 3b2 – 16ac.
Advertisements
Solution
The given quadratic equation is
ax2 + bx + c = 0
Let α be the one root
Then other root = 3α
Now, Sum of the root = `(-b)/a`
⇒ α + 3α = `(-b)/a`
⇒ 4α = `(-b)/a`
⇒ α = `(-b)/(4a)` ...(i)
Also product of the root α x 3α
= `c/a`
= 3α2 = `c/a`
From equation (i) `3(-b/(4a))^2 = c/a`
⇒ `3 xx b^2/(16a^2) = c/a`
⇒ 3b2 = 16ac Proved.
RELATED QUESTIONS
Is it possible to design a rectangular park of perimeter 80 and area 400 m2? If so find its length and breadth.
Find the values of k for which the roots are real and equal in each of the following equation:
x2 - 2kx + 7k - 12 = 0
Solve the following quadratic equation using formula method only
`3"x"^2 +2 sqrt 5 "x" -5 = 0`
Solve the following quadratic equation using formula method only
3x2 + 12 = 32 x
Without actually determining the roots comment upon the nature of the roots of each of the following equations:
x2 - 5x + 7 = 0
Choose the correct answer from the given four options :
If the equation {k + 1)x² – 2(k – 1)x + 1 = 0 has equal roots, then the values of k are
If the roots of px2 + qx + 2 = 0 are reciprocal of each other, then:
Find the nature of the roots of the quadratic equation:
4x2 – 5x – 1 = 0
‘The sum of the ages of a boy and his sister (in years) is 25 and product of their ages is 150. Find their present ages.
The number of integral values of m for which the equation (1 + m2)x2 – 2(1 + 3m)x + (1 + 8m) = 0 has no real root is ______.
