Advertisements
Advertisements
Question
Determine the nature of the roots of the following quadratic equation:
`3/5x^2-2/3x+1=0`
Advertisements
Solution
The given quadric equation is `3/5x^2-2/3x+1=0`
⇒ 9x2 - 10x + 15 = 0
Here, a = 9, b = -10 and c = 15
As we know that D = b2 - 4ac
Putting the value of a = 9, b = -10 and c = 15
D = (-10)2 - 4(9)(15)
= 100 - 540
= -440
Since, D < 0
Therefore, root of the given equation are not real.
APPEARS IN
RELATED QUESTIONS
Is it possible to design a rectangular park of perimeter 80 and area 400 m2? If so find its length and breadth.
Solve for x using the quadratic formula. Write your answer corrected to two significant figures. (x - 1)2 - 3x + 4 = 0
Find the values of k for which the roots are real and equal in each of the following equation:
kx2 + 4x + 1 = 0
Find the values of k for which the roots are real and equal in each of the following equation:
(k + 1)x2 + 2(k + 3)x + (k + 8) = 0
In the following determine the set of values of k for which the given quadratic equation has real roots:
2x2 + kx + 3 = 0
Find the value of the discriminant in the following quadratic equation :
x2 +2x+4=0
Determine the nature of the roots of the following quadratic equation :
2x2 + 5x - 6 = 0
Solve the following quadratic equation using formula method only
`3"x"^2 - 5"x" + 25/12 = 0 `
Find the value(s) of k for which the pair of equations
kx + 2y = 3
3x + 6y = 10 has a unique solution.
(3x - 5)(2x + 7) = 0
Without actually determining the roots comment upon the nature of the roots of each of the following equations:
x2 + 5x + 15 = 0.
Determine whether the given quadratic equations have equal roots and if so, find the roots:
3x2 - 6x + 5 = 0
Discuss the nature of the roots of the following equation: `sqrt(3)x^2 - 2x - sqrt(3)` = 0
Find the value(s) of k for which each of the following quadratic equation has equal roots: (k + 4)x2 + (k + 1)x + 1 =0 Also, find the roots for that value (s) of k in each case.
If the roots of px2 + qx + 2 = 0 are reciprocal of each other, then:
Solve for x: `5/2 x^2 + 2/5 = 1 - 2x`.
‘The sum of the ages of a boy and his sister (in years) is 25 and product of their ages is 150. Find their present ages.
Statement A (Assertion): If 5 + `sqrt(7)` is a root of a quadratic equation with rational co-efficients, then its other root is 5 – `sqrt(7)`.
Statement R (Reason): Surd roots of a quadratic equation with rational co-efficients occur in conjugate pairs.
If one root of the quadratic equation x2 + 12x – k = 0 is thrice the other root, then find the value of k.
Find the value of ‘p’ for which the quadratic equation px(x – 2) + 6 = 0 has two equal real roots.
