Advertisements
Advertisements
प्रश्न
Solve the following quadratic equation using formula method only
3a2x2 +8abx + 4b2 = 0, a ≠ 0
Advertisements
उत्तर
3a2x2 +8abx + 4b2 = 0
`"x"^2 + (8"b")/(3"a") "x" + (4"b"^2)/(3"a"^2) = 0`
a = 1 ; b = `(8"b")/(3"a")` ; c = `(4"b"^2)/(3"a"^2)`
D = b2 - 4ac
= `((8"b")/(3"a"))^2 - 4(1)((4"b"^2)/(3"a"^2))`
= `(64 "b"^2)/(9"a"^2) - (16 "b"^2)/(3"a"^2)`
= `(64"b"^2 - 48 "b"^2)/(9"a"^2) = (16"b"^2)/(9"a"^2)`
x = `(- "b" ± sqrt ("b"^2 - 4 "ac"))/(2a)`
x = `(-(8"b")/(3"a") +- sqrt ((16"b"^2)/(9"a"^2)))/2`
x = `(-(8"b")/(3"a") + (4"b")/(3"a")) / 2` , x = `(-(8"b")/(3"a") - (4"b")/(3"a")) / 2`
x = `(-4"b")/(6"a")` , x = `(- 12"b")/(6"a")`
x = ` - (2"b")/(3"a")` , x =` - (2"b")/"a"`
APPEARS IN
संबंधित प्रश्न
Without solving, examine the nature of roots of the equation 4x2 – 4x + 1 = 0
If the roots of the equations ax2 + 2bx + c = 0 and `bx^2-2sqrt(ac)x+b = 0` are simultaneously real, then prove that b2 = ac.
The equation `3x^2 – 12x + (n – 5) = 0` has equal roots. Find the value of n.
Determine the nature of the roots of the following quadratic equation :
2x2 + x-1=0
Solve the following by reducing them to quadratic equations:
x4 - 26x2 + 25 = 0
Determine whether the given quadratic equations have equal roots and if so, find the roots:
x2 + 5x + 5 = 0
Find the values of k for which each of the following quadratic equation has equal roots: 9x2 + kx + 1 = 0 Also, find the roots for those values of k in each case.
Discuss the nature of the roots of the following equation: 3x2 – 7x + 8 = 0
Mohan and Sohan solve an equation. In solving Mohan commits a mistake in constant term and finds the roots 8 and 2. Sohan commits a mistake in the coefficient of x. The correct roots are:
Find whether the following equation have real roots. If real roots exist, find them.
5x2 – 2x – 10 = 0
