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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
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

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 $k = +30 or -30$

11. The quadratic equation whose one root is $2+\sqrt{3}$ [2070]

x2+4x+1 = 0

x2-4x + 1 = 0

x2 - 4x - 1 = 0

-x2 - 4x - 1 = 0

Solutions
$x = 2 + \sqrt{3}$
$x-2 = \sqrt{3}$
$(x-2)^2 = 3$
$x^2 - 4x + 4 - 3 = 0$
$x^2 - 4x + 1 = 0$
I there is