Question

7. (a)(i) Use completing the square method to solve the general quadratic equation ax^2+bx+c=0. (ii) Hence, use the result to find the roots of 4x^2+7x-2=0. (b) The mean of 6 numbers is 40. Three of the numbers total 90. What is the mean of the remaining 3 numbers? (12 marks)

Accepted Answer

(a)(i) Dividing by a and completing the square gives x = (-b +/- sqrt(b^2-4ac)) / 2a (the quadratic formula).
(ii) For 4x^2+7x-2=0: a=4, b=7, c=-2. x = (-7 +/- sqrt(49+32))/8 = (-7 +/- 9)/8, giving x=1/4 or x=-2.
(b) Sum of all 6 numbers = 6x40=240. Sum of remaining 3 numbers = 240-90=150. Mean of remaining 3 = 150/3 = 50.

NABTEB Mathematics 2025 Theory — Question 7

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