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A day full of math games & activities. Find one near you.
What substitution should be used to rewrite 4x12 - 5x6 - 14 = 0 as a quadratic equation?
u = x2, u = x3, u = x6, u = x12
Solution:
The given quadratic equation is
4x12 - 5x6 - 14 = 0
Let us assume u = x6
4u2 - 5u - 14 = 0
The standard form of the quadratic equation ax2 + bx + c = 0 and the formula used is
x = [-b ± √(b2 - 4ac)]/ 2a
Here a = 4, b = -5 and c = -14
Substituting these values in the formula
x = [-(-5) ± √((-5)2 - 4 × 4 × -14)]/ (2 × 4)
By further simplification
x = [5 ± √(25 + 224)]/ 8
x = [5 ± √249]/ 8
Therefore, u = x6 should be used to rewrite as a quadratic equation.
What substitution should be used to rewrite 4x12 - 5x6 - 14 = 0 as a quadratic equation?
u = x2, u = x3, u = x6, u = x12
Summary:
The substitution u = x6 should be used to rewrite 4x12 - 5x6 - 14 = 0 as a quadratic equation.
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