Advertisements
Advertisements
प्रश्न
Without actually determining the roots comment upon the nature of the roots of each of the following equations:
9a2b2x2 - 48abc + 64c2d2 = 0, a ≠ 0, b ≠ 0
Advertisements
उत्तर
9a2b2x2 - 48abc + 64c2d2 = 0
Here, D = b2 - 4ac
⇒ (-48abcd)2 - 4 x 9a2b2 x 64c2d2
2304a2b2c2d2 - 2304a2b2c2d2 = 0
D = 0
Roots are real and equal.
संबंधित प्रश्न
Without solving, examine the nature of roots of the equation 2x2 – 7x + 3 = 0
If one root of the quadratic equation is `3 – 2sqrt5` , then write another root of the equation.
Solve the following quadratic equation using formula method only
`2x^2 - 2 . sqrt 6x + 3 = 0`
Find if x = – 1 is a root of the equation 2x² – 3x + 1 = 0.
If the ratio of the roots of the equation
lx2 + nx + n = 0 is p: q, Prove that
`sqrt(p/q) + sqrt(q/p) + sqrt(n/l) = 0.`
Discuss the nature of the roots of the following equation: `x^2 - (1)/(2)x - 4` = 0
(x2 + 1)2 – x2 = 0 has:
If the one root of the equation 4x2 – 2x + p – 4 = 0 be the reciprocal of the other. The value of p is:
Does there exist a quadratic equation whose coefficients are all distinct irrationals but both the roots are rationals? Why?
Find the value of ‘c’ for which the quadratic equation
(c + 1) x2 - 6(c + 1) x + 3(c + 9) = 0; c ≠ - 1
has real and equal roots.
