Question
I. 2y2Â + 11y + 15 = 0 II.
3x2Â + 4x - 4= 0Solution
I. 2y2Â + 11y + 15 = 0 2y2Â + 6 y + 5 y + 15 = 0 2y (y + 3) + 5(y + 3) = 0 y = - 3, -5/2 II. 3x2Â + 4x - 4= 0 3x2Â + 6 x - 2 x - 4 = 0 3x (x + 2) - 2(x + 2) = 0 (3x - 2) (x + 2) = 0 x = - 2, 2/3 Hence, x < y. Alternate Method: if signs of quadratic equation is +ve and +ve respectively then the roots of equation will be -ve and -ve. So, roots of first equation = y = -3, -5/2 if signs of quadratic equation is +ve and -ve respectively then the roots of equation will be -ve and +ve. (note: -ve sign will come in larger root) So, roots of second equation = x = -2, 2/3 After comparing roots of quadratice eqution we can conclude that x > y.
There are 6 blue pens, 5 black pens and 4 green pens in a bag. Three pens are chosen randomly.
Quantity I – The probability of their being...
If x4 + 2x3 + ax2 + bx + 9 is a perfect square, where a and b are positive real numbers, then the value of a and b are
If x + y = 7 and xy = 10, then the value of (1/x3 + 1/x3) is :
If 0 ≤ θ ≤ 90°, and sec107 θ + cos107 θ = 2, then. (secθ + cosθ) is equal to:
Which is the largest six digit number, which when divided by 12, 15, 20, 24 and 30, leaves the remainders 8, 11, 16, 20 and 26 respectively.
If a3 = 117 + b3 and a = 3 + b, then the value of a + b is:
If (a + b)/c = 6/5 and (b + c)/a = 9/2, then what is the value of (a + c)/b?
If 8x2 + y2 − 12x − 4xy + 9 = 0, then the value of (14x − 5y) is :
The total number of even factors of 25 × 33 × 52 is:
If -5 ≤ x ≤ 3 and -1 ≤ y ≤ 0, then the minimum value of 2y – 3x is: