Advertisements
Advertisements
प्रश्न
If one root of the quadratic equation ax2 + bx + c = 0 is double the other, prove that 2b2 = 9 ac.
उत्तर
ax2 + bx + c = 0.
Let the roots be α and 2α
Sum of roots = `(-b)/a`
⇒ α + 2α = `(-b)/a`
⇒ 3α = `(-b)/a`
⇒ α = `-(b)/(3a)` ...(i)
Product of root = `c/a`
⇒ 2α2 = `c/a`
α2 = `c/(2a), α = sqrt(c/(2a)` ...(iii)
Equation (i) = (ii)
`(-b)/(3a) = sqrt(c/(2a)) ...("squaring both side")`
`b^2/(9a^2) = c/(2a)`
⇒ 2b2 = 9ac.
Hence Proved.
APPEARS IN
संबंधित प्रश्न
Find the values of k for which the roots are real and equal in each of the following equation:
(k + 1)x2 - 2(3k + 1)x + 8k + 1 = 0
Solve the following quadratic equation using formula method only
`"x"^2 + 1/2 "x" = 3`
Without solving the following quadratic equation, find the value of ‘p’ for which the given equation has real and equal roots:
x² + (p – 3) x + p = 0
Discuss the nature of the roots of the following quadratic equations : -2x2 + x + 1 = 0
Choose the correct answer from the given four options :
If the equation 2x² – 5x + (k + 3) = 0 has equal roots then the value of k is
Choose the correct answer from the given four options :
If the equation 3x² – kx + 2k =0 roots, then the the value(s) of k is (are)
If the roots of the given quadratic equation are real and equal, then find the value of ‘m’.
(m – 12)x2 + 2(m – 12)x + 2 = 0
If –5 is a root of the quadratic equation 2x2 + px – 15 = 0, then:
Every quadratic equation has at least two roots.
Every quadratic equations has at most two roots.
