Advertisements
Advertisements
प्रश्न
Find the nature of the roots of the following quadratic equations: `x^2 - (1)/(2)x - (1)/(2)` = 0
Advertisements
उत्तर
`x^2 - (1)/(2)x - (1)/(2)` = 0
Here `a = 1, b = -(1)/(2), c = -(1)/(2)`
∴ D = b2 - 4ac
= `((-1)/2)^2 - 4 xx 1 xx ((-1)/2)`
= `(1)/(4) + 2`
= `(9)/(4)`
∴ D = `(9)/(4) > 0`
∴ Roots are real and unequal.
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(k - 1)x + 1 = 0
If the roots of the equation (a2 + b2)x2 − 2 (ac + bd)x + (c2 + d2) = 0 are equal, prove that `a/b=c/d`.
Prove that both the roots of the equation (x - a)(x - b) +(x - b)(x - c)+ (x - c)(x - a) = 0 are real but they are equal only when a = b = c.
If the equation \[\left( 1 + m^2 \right) x^2 + 2 mcx + \left( c^2 - a^2 \right) = 0\] has equal roots, prove that c2 = a2(1 + m2).
Solve the following quadratic equation using formula method only :
16x2 = 24x + 1
Solve the following quadratic equation using formula method only
`3"x"^2 - 5"x" + 25/12 = 0 `
Solve the following quadratic equation using formula method only
`"x"^2 + 1/2 "x" - 1 = 0`
Form the quadratic equation whose roots are:
`2 + sqrt(5) and 2 - sqrt(5)`.
Discuss the nature of the roots of the following equation: `5x^2 - 6sqrt(5)x + 9` = 0
Find whether the following equation have real roots. If real roots exist, find them.
5x2 – 2x – 10 = 0
