If x+y=7 and xy=19, then calculate the value of x²+y².

If one of the zeroes of a cubic polynomial x³ + ax² + bx + c is 1, then the product of the other two zeroes is:

If x + 1 is a factor of 2x³ + ax² + 2bx + 1, and 2a – 3b = 4, then the value of a + 2b is:

The solution of the pair of equations $$\frac{b}{a}x + \frac{a}{b}y = a^2 + b^2$$​ and x + y = 2ab is:

If the roots of the equation x³ − 12x² + 39x − 28 = 0 are in A.P., then their common difference is:

Both the roots of the equation (x − a)(x − b) + (x − b)(x − c) + (x − c)(x − a) = 0 are always:

The value of ‘a’ for which one root of the quadratic equation (a² − 5a + 3)x² + (3a − 1)x + 2 = 0 is twice the other, is:

​Simplify: $$3 \left( (\frac{7}{3}) x^2 - 27x + 14 \right) - 7 \left( x^2 + 8x - 11 \right)$$​​

Find roots of 5m² + 18m + 16 = 0 

Find roots of 4m² + 6m + 2 = 0

If sum and product of the roots of a quadratic equation are $$(4-3\sqrt{2})$$ and –28, respectively, then find the quadratic equation.​