Advertisements
Advertisements
प्रश्न
Determine the nature of the roots of the following quadratic equation :
2x2 + x-1=0
Advertisements
उत्तर
2x2 + x-1=0
b2 - 4ac
= (1)2-4(2)(-1)
= 1+ 8
=9
Since 9 is a perfect square and greater than 0, hence the roots are real and rational.
APPEARS IN
संबंधित प्रश्न
If the quadratic equation px2 − 2√5px + 15 = 0 has two equal roots then find the value of p.
Find the nature of the roots of the following quadratic equation. If the real roots exist, find them:
2x2 - 6x + 3 = 0
Solve the following equation:
`x - 18/x = 6` Give your answer correct to two significant figures.
Find the values of k for which the roots are real and equal in each of the following equation:
(2k + 1)x2 + 2(k + 3)x + (k + 5) = 0
Solve for x : `9^(x + 2) -6.3^(x + 1) + 1 = 0`.
Find the discriminant of the following equations and hence find the nature of roots: 3x2 + 2x - 1 = 0
Find the value(s) of m for which each of the following quadratic equation has real and equal roots: (3m + 1)x2 + 2(m + 1)x + m = 0
If (1 – p) is a root of the equation x2 + px + 1 – p = 0, then roots are:
State whether the following quadratic equation have two distinct real roots. Justify your answer.
(x + 1)(x – 2) + x = 0
If α and β are the distinct roots of the equation `x^2 + (3)^(1/4)x + 3^(1/2)` = 0, then the value of α96(α12 – 1) + β96(β12 – 1) is equal to ______.
