Advertisements
Advertisements
प्रश्न
State whether the following quadratic equation have two distinct real roots. Justify your answer.
`(x - sqrt(2))^2 - 2(x + 1) = 0`
उत्तर
The equation `(x - sqrt(2))^2 - 2(x + 1)` = 0 has two distinct and real roots.
Simplifying the above equation,
`x^2 - 2sqrt(2)x + 2 - sqrt(2)x - sqrt(2)` = 0
`x^2 - sqrt(2)(2 + 1)x + (2 - sqrt(2))` = 0
`x^2 - 3sqrt(2)x + (2 - sqrt(2))` = 0
D = b2 – 4ac
= `(- 3sqrt(2))^2 - 4(1)(2 - sqrt(2))`
= `18 - 8 + 4sqrt(2) > 0`
Hence, the roots are real and distinct.
APPEARS IN
संबंधित प्रश्न
Find the values of k for the following quadratic equation, so that they have two equal roots.
kx (x - 2) + 6 = 0
Solve for x using the quadratic formula. Write your answer corrected to two significant figures. (x - 1)2 - 3x + 4 = 0
For what value of k, (4 - k)x2 + (2k + 4)x + (8k + 1) = 0, is a perfect square.
Show that the equation 2(a2 + b2)x2 + 2(a + b)x + 1 = 0 has no real roots, when a ≠ b.
Write the value of k for which the quadratic equation x2 − kx + 4 = 0 has equal roots.
Find the value of the discriminant in the following quadratic equation :
10 x - `1/x` = 3
Determine the nature of the roots of the following quadratic equation :
x2 -5x+ 7= 0
Solve the following quadratic equation using formula method only :
x2 +10x- 8= 0
Solve the following quadratic equation using formula method only
4 - 11 x = 3x2
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
