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Consider the statements given below: A: Sum of roots of a quadratic equation ax2 + bx + c = 0 is (c/a). B: If one root of a quadratic equation is (p + qi), then root must be (q + pi). C: Roots of the equation 3x2 + 4x = 5 are all real. Which of the statement(s) is/are TRUE?
In the following question, two statements are given each followed by two conclusions I and II. You have to consider the statements to be true even if theyseem to be at variance from commonly known facts. You have to decide which of the given conclusions, if any, follows from the given statements. Statements:
(I) Some polynomials are linear equations.
(II) Some linear equations are quadratic. Conclusion:
(I) Polynomials are quadratic.
(II) Linear equations are quadratic.
If the roots of the quadratic equation x2 – x + 1 = 0 are α and β, then find the quadratic equation whose roots are α4 and β4.
A and B are positive roots of quadratic equation and (A + B)2 = 400 and (A – B)2 = 4. Find the quadratic equation whose roots are A and B.
 If sum of zeroes of a quadratic equation is 4 and product of zeroes is (-5). What is the quadratic equation?
The product of the roots of a quadratic equation is 20 and the sum of its roots is (-8). What is the quadratic equation?
If α and β are two zeros of quadratic equation 63x2 – 46x + 8 = 0, then what is a quadratic equation whose zeros are 7α and 9β?
The sum and the product of the roots of a quadratic equation are 7 and 12 respectively. If the bigger root is halved and the smaller root is doubled, then what is the resulting quadratic equation ?
If -5 is a root of the quadratic equation 2x2 + px - 15 = 0 and also of the quadratic equation p(kx2 + x) = 0, then what are the values of p and k?
If sum of the roots of a quadratic equation is ­-7 and product of the roots is 12. Find the quadratic equation.