bcafamilyQuadratic Equations
15. The quadratic equation whose roots are 3 and 4 is [2075]
x2 - 7x - 12 = 0
x2 - 7x + 12 = 0
x2 + 7x + 12 = 0
x2 + 7x - 12 = 0
Solutions
Let α = 3 and β = 4
α + β = 3 + 4 = 7
α × β = 3 × 4 = 12
The required Quadratic Equation is
x2 - α + β.x +α.β=0
x2 -7x+12=0
α + β = 3 + 4 = 7
α × β = 3 × 4 = 12
The required Quadratic Equation is
x2 - α + β.x +α.β=0
x2 -7x+12=0
15. Quadratic equation whose roots are -3 and n is [2074]
x2 + x - 6 = 9
x2 + x + 6
x2 - x - 6 = 0
x2 - x + 6 = 0
15. If one root of 5x2 + 2x - k = 0 is the reciprocal of the other than k = [2073]
-5
5
2/5
5/2
Solutions
P(X) = 5x²+2x-k
Here,
A = 5 , B = 13 and C= K
Product of roots = C/A = -k/5
$ {α ×{ 1\over α}} = 1$
k = -5
Here,
A = 5 , B = 13 and C= K
Product of roots = C/A = -k/5
$ {α ×{ 1\over α}} = 1$
k = -5
10. The system of equation 2x + y = 5; 4x + 2 = 8 is [2072]
Consistent and dependent
Inconsistent and Independent
Inconsistent and dependent
Consistent and independent
10. For what value of k will the equation 5x2 - kx + 45 = 0 have equal roots? [2070]
0
± 3
± 30
± 33
Solutions
$b^2 - 4ac = 0 $
In this case $ a = 5 b = -k and c = 45$
so $-k^2 - 4 * 5 * 45 = 0 $
$ -k^2 - 900 = 0 $
$-k^2 = 900 $
$ k = ±√900$
so $k = +30 or -30$
In this case $ a = 5 b = -k and c = 45$
so $-k^2 - 4 * 5 * 45 = 0 $
$ -k^2 - 900 = 0 $
$-k^2 = 900 $
$ k = ±√900$
so $k = +30 or -30$
11. The quadratic equation whose one root is [2070]
x2+4x+1 = 0
x2-4x + 1 = 0
x2 - 4x - 1 = 0
-x2 - 4x - 1 = 0
Solutions
$x = 2 + \sqrt{3} $
$x-2 = \sqrt{3}$
$(x-2)^2 = 3$
$x^2 - 4x + 4 - 3 = 0$
$x^2 - 4x + 1 = 0$
$x-2 = \sqrt{3}$
$(x-2)^2 = 3$
$x^2 - 4x + 4 - 3 = 0$
$x^2 - 4x + 1 = 0$
