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
Solve the equation by using the formula method. 3y2 +7y + 4 = 0
Solve the following quadratic equation for x :
9x2 − 6b2x − (a4 − b4) = 0
Find the value of p for which the quadratic equation (2p + 1)x2 − (7p + 2)x + (7p − 3) = 0 has equal roots. Also find these roots.
Find the values of k for which the roots are real and equal in each of the following equation:
4x2 - 2(k + 1)x + (k + 4) = 0
For what value of k, the roots of the equation x2 + 4x + k = 0 are real?
Find the nature of the roots of the following quadratic equations: `x^2 - 2sqrt(3)x - 1` = 0 If real roots exist, find them.
The quadratic equation whose roots are 1:
The roots of the equation (b – c) x2 + (c – a) x + (a – b) = 0 are equal, then:
If p, q and r are rational numbers and p ≠ q ≠ r, then roots of the equation (p2 – q2)x2 – (q2 – r2)x + (r2 – p2) = 0 are:
Does there exist a quadratic equation whose coefficients are all distinct irrationals but both the roots are rationals? Why?
