Advertisements
Advertisements
प्रश्न
State whether the following quadratic equation have two distinct real roots. Justify your answer.
3x2 – 4x + 1 = 0
उत्तर
The equation 3x2 – 4x + 1 = 0 has two real and distinct roots.
D = b2 – 4ac
= (–4)2 – 4(3)(1)
= 16 – 12 > 0
Hence, the roots are real and distinct.
APPEARS IN
संबंधित प्रश्न
Find the nature of the roots of the following quadratic equation. If the real roots exist, find them:
2x2 - 3x + 5 = 0
Determine the nature of the roots of the following quadratic equation:
2(a2 + b2)x2 + 2(a + b)x + 1 = 0
Solve the following quadratic equation using formula method only
`2x^2 - 2 . sqrt 6x + 3 = 0`
Find the value of k for which the roots of the equation 3x2 -10x +k = 0 are reciprocal of each other.
Find the value(s) of k for which the pair of equations
kx + 2y = 3
3x + 6y = 10 has a unique solution.
Without actually determining the roots comment upon the nature of the roots of each of the following equations:
x2 - 5x + 7 = 0
Discuss the nature of the roots of the following quadratic equations : `2sqrt(3)x^2 - 5x + sqrt(3)` = 0
Find the nature of the roots of the following quadratic equations: `x^2 - (1)/(2)x - (1)/(2)` = 0
For the roots of the equation a – bx – x2 = 0; (a > 0, b > 0), which statement is true?
If x = 3 is one of the roots of the quadratic equation x2 – 2kx – 6 = 0, then the value of k is ______.
