Advertisements
Advertisements
प्रश्न
State whether the following quadratic equation have two distinct real roots. Justify your answer.
x2 – 3x + 4 = 0
Advertisements
उत्तर
The equation x2 – 3x + 4 = 0 has no real roots.
D = b2 – 4ac
= (–3)2 – 4(1)(4)
= 9 – 16 < 0
Hence, the roots are imaginary.
APPEARS IN
संबंधित प्रश्न
Find the nature of the roots of the following quadratic equation. If the real roots exist, find them:
2x2 - 6x + 3 = 0
If one root of the quadratic equation is `3 – 2sqrt5` , then write another root of the equation.
Find the value of p, for which one root of the quadratic equation px2 – 14x + 8 = 0 is 6 times the other.
Determine the nature of the roots of the following quadratic equation:
2(a2 + b2)x2 + 2(a + b)x + 1 = 0
In the following determine the set of values of k for which the given quadratic equation has real roots:
3x2 + 2x + k = 0
Determine the nature of the roots of the following quadratic equation :
x2 -4x + 4=0
Determine the nature of the roots of the following quadratic equation :
x2 +3x+1=0
Solve the following quadratic equation using formula method only :
16x2 = 24x + 1
Solve the following quadratic equation using formula method only
3x2 + 12 = 32 x
In each of the following, determine whether the given numbers are roots of the given equations or not; 3x2 – 13x – 10 = 0; 5, `(-2)/(3)`
In each of the following, determine whether the given numbers are roots of the given equations or not; 6x2 – x – 2 = 0; `(-1)/(2), (2)/(3)`
Find the discriminant of the following equations and hence find the nature of roots: 2x2 + 15x + 30 = 0
Discuss the nature of the roots of the following quadratic equations : -2x2 + x + 1 = 0
Without solving the following quadratic equation, find the value of ‘p’ for which the given equations have real and equal roots: px2 – 4x + 3 = 0
If the roots of the equations ax2 + 2bx + c = 0 and `"bx"^2 - 2sqrt"ac" "x" + "b" = 0` are simultaneously real, then
Equation (x + 1)2 – x2 = 0 has ____________ real root(s).
If the coefficient of x2 and the constant term of a quadratic equation have opposite signs, then the quadratic equation has real roots.
Find the value of 𝑚 so that the quadratic equation 𝑚𝑥(5𝑥 − 6) = 0 has two equal roots.
Assertion (A): If one root of the quadratic equation 4x2 – 10x + (k – 4) = 0 is reciprocal of the other, then value of k is 8.
Reason (R): Roots of the quadratic equation x2 – x + 1 = 0 are real.
The roots of the quadratic equation px2 – qx + r = 0 are real and equal if ______.
