Advertisements
Advertisements
प्रश्न
Without actually determining the roots comment upon the nature of the roots of each of the following equations:
x2 - 5x + 7 = 0
Advertisements
उत्तर
x2 - 5x + 7 = 0
Here, a = 1, b = -5 and c = 7
D = b2 - 4ac
⇒ 25 - 4 x 1 x 7.
⇒ 25 - 28
= -3
Since D < 0 roots are imaginary.
संबंधित प्रश्न
If -5 is a root of the quadratic equation 2x2 + px – 15 = 0 and the quadratic equation p(x2 + x)k = 0 has equal roots, find the value of k.
Find the values of k for which the given quadratic equation has real and distinct roots:
kx2 + 6x + 1 = 0
Determine, if 3 is a root of the given equation
`sqrt(x^2 - 4x + 3) + sqrt(x^2 - 9) = sqrt(4x^2 - 14x + 16)`.
Solve x2/3 + x1/3 - 2 = 0.
Determine whether the given quadratic equations have equal roots and if so, find the roots:
x2 + 5x + 5 = 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.`
Which of the following equations has no real roots?
A natural number, when increased by 12, equals 160 times its reciprocal. Find the number.
State whether the following quadratic equation have two distinct real roots. Justify your answer.
3x2 – 4x + 1 = 0
Every quadratic equation has exactly one root.
