Advertisements
Advertisements
Question
Determine the nature of the roots of the following quadratic equation :
x2 -5x+ 7= 0
Advertisements
Solution
x2 -5x+ 7= 0
b2 - 4ac
= (-5)2 - 4(1)(7)
= 25 - 28
= -3
Since discriminant is negative, hence the roots are imaginary.
APPEARS IN
RELATED QUESTIONS
Solve the equation by using the formula method. 3y2 +7y + 4 = 0
In each of the following, determine whether the given numbers are roots of the given equations or not; x2 – x + 1 = 0; 1, – 1
Find the discriminant of the following equations and hence find the nature of roots: 3x2 – 5x – 2 = 0
If α and β are the roots of the equation 2x2 – 3x – 6 = 0. The equation whose roots are `1/α` and `1/β` is:
The equation 12x2 + 4kx + 3 = 0 has real and equal roots, if:
Every quadratic equations has at most two roots.
Complete the following activity to determine the nature of the roots of the quadratic equation x2 + 2x – 9 = 0 :
Solution :
Compare x2 + 2x – 9 = 0 with ax2 + bx + c = 0
a = 1, b = 2, c = `square`
∴ b2 – 4ac = (2)2 – 4 × `square` × `square`
Δ = 4 + `square` = 40
∴ b2 – 4ac > 0
∴ The roots of the equation are real and unequal.
The nature of roots of the quadratic equation 9x2 – 6x – 2 = 0 is ______.
The roots of the quadratic equation px2 – qx + r = 0 are real and equal if ______.
The roots of the quadratic equation x2 – 6x – 7 = 0 are ______.
