Advertisements
Advertisements
प्रश्न
Find the discriminant of the following equations and hence find the nature of roots: 3x2 – 5x – 2 = 0
उत्तर
3x2 – 5x – 2 = 0
Here a = 3, b = -5, c = -2
∴ D = b2 - 4ac
= (-5)2 - 4 x 3 x (-2)
= 25 + 24
= 49
∴ Discriminant = 49
∴ D > 0
∵ Roots are real and distinct.
APPEARS IN
संबंधित प्रश्न
Form the quadratic equation if its roots are –3 and 4.
Find the values of k for which the roots are real and equal in each of the following equation:
x2 - 2(5 + 2k)x + 3(7 + 10k) = 0
Find the values of k for which the roots are real and equal in each of the following equation:
kx(x - 2) + 6 = 0
If the roots of the equation (b - c)x2 + (c - a)x + (a - b) = 0 are equal, then prove that 2b = a + c.
In each of the following determine the; value of k for which the given value is a solution of the equation:
kx2 + 2x - 3 = 0; x = 2
Discuss the nature of the roots of the following equation: `x^2 - (1)/(2)x - 4` = 0
The roots of the quadratic equation 6x2 – x – 2 = 0 are:
The roots of the quadratic equation `1/("a" + "b" + "x") = 1/"a" + 1/"b" + 1/"x"`, a + b ≠ 0 is:
State whether the following quadratic equation have two distinct real roots. Justify your answer.
`2x^2 - 6x + 9/2 = 0`
If the coefficient of x2 and the constant term have the same sign and if the coefficient of x term is zero, then the quadratic equation has no real roots.