Advertisements
Advertisements
प्रश्न
State whether the following quadratic equation have two distinct real roots. Justify your answer.
2x2 + x – 1 = 0
उत्तर
The equation 2x2 + x – 1 = 0 has two real and distinct roots.
D = b2 – 4ac
= 12 – 4(2)(–1)
= 1 + 8 > 0
Hence, the roots are real and distinct.
APPEARS IN
संबंधित प्रश्न
Solve for x: `1/(x+1)+2/(x+2)=4/(x+4), `x ≠ -1, -2, -3
Solve the quadratic equation 2x2 + ax − a2 = 0 for x.
If the roots of the equation (c2 – ab) x2 – 2 (a2 – bc) x + b2 – ac = 0 in x are equal, then show that either a = 0 or a3 + b3 + c3 = 3abc
`(2)/x^2 - (5)/x + 2` = 0
Solve for x : `9^(x + 2) -6.3^(x + 1) + 1 = 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.`
Find the discriminant of the following equations and hence find the nature of roots: 3x2 – 5x – 2 = 0
The quadratic equation `2x^2 - sqrt(5)x + 1 = 0` has ______.
Complete the following activity to find the value of discriminant for quadratic equation 4x2 – 5x + 3 = 0.
Activity: 4x2 – 5x + 3 = 0
a = 4 , b = ______ , c = 3
b2 – 4ac = (– 5)2 – (______) × 4 × 3
= ( ______ ) – 48
b2 – 4ac = ______
If (1 – p) is a root of the equation x2 + px + 1 – p = 0, then roots are:
