Advertisements
Advertisements
Question
Which of the following equations has 2 as a root?
Options
x2 – 4x + 5 = 0
x2 + 3x – 12 = 0
2x2 – 7x + 6 = 0
3x2 – 6x – 2 = 0
Solution
2x2 – 7x + 6 = 0
Explanation:
(A) Substituting x = 2 in x2 – 4x + 5, we get
(2)2 – 4(2) + 5
= 4 – 8 + 5
= 1 ≠ 0
So, x = 2 is not a root of x2 – 4x + 5 = 0
(B) Substituting x = 2 in x2 + 3x – 12, we get
2)2 + 3(2) – 12
= 4 + 6 – 12
= –2 ≠ 0
So, x = 2 is not a root of x2 + 3x – 12 = 0
(C) Substituting x = 2 in 2x2 – 7x + 6, we get
2(2)2 – 7(2) + 6
= 8 – 14 + 6
= 14 – 14
= 0
So, x = 2 is a root of 2x2 – 7x + 6 = 0
(D) Substituting x = 2 in 3x2 – 6x – 2, we get
3(2)2 – 6(2) – 2
= 12 – 12 – 2
= –2 ≠ 0
So, x = 2 is not a root of 3x2 – 6x – 2 = 0
APPEARS IN
RELATED QUESTIONS
If x=−`1/2`, is a solution of the quadratic equation 3x2+2kx−3=0, find the value of k
Find that non-zero value of k, for which the quadratic equation kx2 + 1 − 2(k − 1)x + x2 = 0 has equal roots. Hence find the roots of the equation.
Without solving, examine the nature of roots of the equation 4x2 – 4x + 1 = 0
If one root of the quadratic equation is `3 – 2sqrt5` , then write another root of the equation.
Find the values of k for which the roots are real and equal in each of the following equation:
(3k+1)x2 + 2(k + 1)x + k = 0
Find the values of k for which the given quadratic equation has real and distinct roots:
kx2 + 2x + 1 = 0
Find the positive value(s) of k for which quadratic equations x2 + kx + 64 = 0 and x2 – 8x + k = 0 both will have real roots ?
Find the value of the discriminant in the following quadratic equation:
x2 +2x-2=0
Determine the nature of the roots of the following quadratic equation :
4x2 - 8x + 5 = 0
Solve the following quadratic equation using formula method only
`2x^2 - 2 . sqrt 6x + 3 = 0`
Solve the following quadratic equation using formula method only
`3"x"^2 +2 sqrt 5 "x" -5 = 0`
Form the quadratic equation whose roots are:
`2 + sqrt(5) and 2 - sqrt(5)`.
Solve the following by reducing them to quadratic equations:
z4 - 10z2 + 9 = 0.
Find the values of k so that the sum of tire roots of the quadratic equation is equal to the product of the roots in each of the following:
kx2 + 2x + 3k = 0
If one root of the quadratic equation ax2 + bx + c = 0 is double the other, prove that 2b2 = 9 ac.
Choose the correct answer from the given four options :
If the equation 3x² – kx + 2k =0 roots, then the the value(s) of k is (are)
The roots of the quadratic equation `"x" + 1/"x" = 3`, x ≠ 0 are:
If the one root of the equation 4x2 – 2x + p – 4 = 0 be the reciprocal of the other. The value of p is:
If α, β are roots of the equation x2 + px – q = 0 and γ, δ are roots of x2 + px + r = 0, then the value of (α – y)(α – δ) is ______.
Find the value of ‘c’ for which the quadratic equation
(c + 1) x2 - 6(c + 1) x + 3(c + 9) = 0; c ≠ - 1
has real and equal roots.
