Advertisements
Advertisements
प्रश्न
Determine the nature of the roots of the following quadratic equation:
`3/5x^2-2/3x+1=0`
उत्तर
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
संबंधित प्रश्न
Find the values of k for which the quadratic equation (3k + 1) x2 + 2(k + 1) x + 1 = 0 has equal roots. Also, find the roots.
If the roots of the equation (b - c)x2 + (c - a)x + (a - b) = 0 are equal, then prove that 2b = a + c.
If a, b, c are real numbers such that ac ≠ 0, then show that at least one of the equations ax2 + bx + c = 0 and -ax2 + bx + c = 0 has real roots.
For what values of k, the roots of the equation x2 + 4x +k = 0 are real?
If one root of the quadratic equation ax2 + bx + c = 0 is double the other, prove that 2b2 = 9 ac.
In each of the following, determine whether the given numbers are roots of the given equations or not; x2 – 5x + 6 = 0; 2, – 3
Discuss the nature of the roots of the following quadratic equations : x2 – 4x – 1 = 0
If one root of the equation x2+ px + 12 = 0 is 4, while the equation x2 + px + q = 0 has equal roots, the value of q is:
A natural number, when increased by 12, equals 160 times its reciprocal. Find the number.
The number of integral values of m for which the equation (1 + m2)x2 – 2(1 + 3m)x + (1 + 8m) = 0 has no real root is ______.
