Advertisements
Advertisements
प्रश्न
If the equation 9x2 + 6kx + 4 = 0 has equal roots, then the roots are both equal to
पर्याय
± `2/3`
± `3/2`
0
±3
Advertisements
उत्तर
Given, quadratic equation is: 9x2 + 6kx + 4 = 0
Now, the given equation has equal roots, so D = 0
⇒ b2 - 4ac = 0
⇒ (6k)2 - 4 × 9 × 4 = 0
⇒ 36k2 - 36 × 4 = 0
⇒ 36k2 = 36 × 4
⇒ k2 = 4
⇒ k = ± 2
Case 1: When k = 2, we have the quadratic equation as:
9x2 + 6(2)x + 4 = 0
⇒ 9x2 + 12x + 4 = 0
⇒ (3x)2 + 2 × 2 × 3x + (2)2 = 0
⇒ (3x + 2)2 = 0
⇒ 3x + 2 = 0
⇒ x = -`2/3`
Case 2: When k = -2, we have the quadratic equation as:
9x2 + 6(-2)x + 4 = 0
⇒ 9x2 - 12x + 4 = 0
⇒ (3x)2 - 2 × 2 × 3x + (2)2 = 0
⇒ (3x - 2)2 = 0
⇒ 3x - 2 = 0
⇒ x = `2/3`
So, two roots of the quadratic equation are `2/3 and -2/3 or ±2/3`.
APPEARS IN
संबंधित प्रश्न
Solve the equation `4/x-3=5/(2x+3); xne0,-3/2` for x .
Find the roots of the following quadratic equation by factorisation:
`sqrt2 x^2 +7x+ 5sqrt2 = 0`
Solve for x
`(x - 1)/(2x + 1) + (2x + 1)/(x - 1) = 2, "where x" != -1/2, 1`
Solve the following quadratic equations by factorization:
`(x-3)/(x+3)-(x+3)/(x-3)=48/7` , x ≠ 3, x ≠ -3
Solve the following quadratic equations by factorization:
`3x^2-2sqrt6x+2=0`
The hypotenuse of a right triangle is 25 cm. The difference between the lengths of the other two sides of the triangle is 5 cm. Find the lengths of these sides.
Find k if x = 3 is a root of equation kx2 – 10x + 3 = 0.
Solve the following quadratic equation by factorisation.
7m2 = 21m
Solve the following quadratic equations by factorization: \[\frac{x + 1}{x - 1} + \frac{x - 2}{x + 2} = 4 - \frac{2x + 3}{x - 2}; x \neq 1, - 2, 2\]
Solve the following quadratic equations by factorization:
\[3\left( \frac{3x - 1}{2x + 3} \right) - 2\left( \frac{2x + 3}{3x - 1} \right) = 5; x \neq \frac{1}{3}, - \frac{3}{2}\]
The number of quadratic equations having real roots and which do not change by squaring their roots is
If the sum of the roots of the equation \[x^2 - \left( k + 6 \right)x + 2\left( 2k - 1 \right) = 0\] is equal to half of their product, then k =
Solve the following equation: `("a+b")^2 "x"^2 - 4 "abx" - ("a - b")^2 = 0`
The product of a girl's age five years ago and her age 3 years later is 105. Find her present age.
Divide 29 into two parts so that the sum of the square of the parts is 425.
One fourth of a herd of camels was seen in the forest. Twice the square root of the herd had gone to mountains and the remaining 15 camels were seen on the bank of a river. Find the total number of camels.
Find two consecutive natural numbers such that the sum of their squares is 61.
A piece of cloth costs Rs. 300. If the piece was 5 metres longer and each metre of cloth costs Rs. 2 less, the cost of the piece would have remained unchanged. How long is the original piece of cloth and what is the rate per metre?
Ritu bought a saree for Rs. 60x and sold it for Rs. (500 + 4x) at a loss of x%. Find the cost price.
For equation `1/x + 1/(x - 5) = 3/10`; one value of x is ______.
