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Q62 (CISF/2022) Science & Technology › Basic Science (Physics, Chemistry, Biology)

If a and B are the roots of the equation x2- 7x + 11 = 0, then the value of x3 + p3 is equal to :

Explanation

For a quadratic equation of the form ax2 + bx + c = 0, the sum of the roots (α + β) is given by -b/a and the product of the roots (αβ) is given by c/a.

Given the equation x2 - 7x + 11 = 0:
Sum of roots (a + B) = -(-7)/1 = 7
Product of roots (aB) = 11/1 = 11

The question asks for the value of the sum of the cubes of the roots (expressed as x3 + p3 due to typographical errors in the source). Using the algebraic identity for the sum of cubes:
a3 + B3 = (a + B)3 - 3aB(a + B)

Substituting the known values:
a3 + B3 = (7)3 - 3(11)(7)
a3 + B3 = 343 - 231 = 112

Therefore, the value is 112, which matches option A.

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