Advertisements
Advertisements
Question
State whether the following quadratic equation have two distinct real roots. Justify your answer.
`(x - sqrt(2))^2 - 2(x + 1) = 0`
Advertisements
Solution
The equation `(x - sqrt(2))^2 - 2(x + 1)` = 0 has two distinct and real roots.
Simplifying the above equation,
`x^2 - 2sqrt(2)x + 2 - sqrt(2)x - sqrt(2)` = 0
`x^2 - sqrt(2)(2 + 1)x + (2 - sqrt(2))` = 0
`x^2 - 3sqrt(2)x + (2 - sqrt(2))` = 0
D = b2 – 4ac
= `(- 3sqrt(2))^2 - 4(1)(2 - sqrt(2))`
= `18 - 8 + 4sqrt(2) > 0`
Hence, the roots are real and distinct.
APPEARS IN
RELATED QUESTIONS
Solve the following quadratic equation by using formula method: 5m2 + 5m – 1 = 0
Is the following situation possible? If so, determine their present ages. The sum of the ages of two friends is 20 years. Four years ago, the product of their ages in years was 48.
In the following determine the set of values of k for which the given quadratic equation has real roots:
kx2 + 6x + 1 = 0
Find the value(s) of k so that the quadratic equation 3x2 − 2kx + 12 = 0 has equal roots ?
Write the value of k for which the quadratic equation x2 − kx + 4 = 0 has equal roots.
Determine the nature of the roots of the following quadratic equation :
x2 +3x+1=0
Solve the following quadratic equation using formula method only
3x2 + 12 = 32 x
Form the quadratic equation whose roots are:
`sqrt(3) and 3sqrt(3)`
Without actually determining the roots comment upon the nature of the roots of each of the following equations:
9a2b2x2 - 48abc + 64c2d2 = 0, a ≠ 0, b ≠ 0
Without actually determining the roots comment upon the nature of the roots of each of the following equations:
x2 - 4x + 1 = 0
If `(2)/(3)` and – 3 are the roots of the equation px2+ 7x + q = 0, find the values of p and q.
Find the discriminant of the following equations and hence find the nature of roots: 3x2 + 2x - 1 = 0
Discuss the nature of the roots of the following quadratic equations : x2 – 4x – 1 = 0
Discuss the nature of the roots of the following equation: 3x2 – 7x + 8 = 0
The roots of the quadratic equation 6x2 – x – 2 = 0 are:
If the roots of the equations ax2 + 2bx + c = 0 and `"bx"^2 - 2sqrt"ac" "x" + "b" = 0` are simultaneously real, then
Find the roots of the quadratic equation by using the quadratic formula in the following:
–x2 + 7x – 10 = 0
Find the nature of the roots of the quadratic equation:
4x2 – 5x – 1 = 0
Equation 2x2 – 3x + 1 = 0 has ______.
