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1 answer:
Solution
Given the quadratic equation:
x² + 2x + 7 = 21
x² + 2x + 7 - 21 = 0
x² + 2x - 14 = 0
a = 1, b = 2, c = - 14
(1) The number of solutions of a given quadratic equation is determine by the discriminant.
From the given values;
(2)² - 4(1 x -14) = 4 + 56 = 60
60 > 0 ( 2 solutions)
1 positive solution and 1 negative solution
Thus, number of positive solutions to this equation is one
(2) The greatest solution or positive solution to the equation is calculated as;
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The solutions of the quadratic equation x² - 5x - 36 = 0 are -4 and 9.
The graph is attached below.
- We are given a quadratic function.
- A polynomial equation of degree two in one variable is a quadratic equation.
- The function given to us is :
- y = x² - 5x - 36
- We need to find the solution of the quadratic function.
- To find the roots, let y = 0.
- x² - 5x - 36 = 0
- Use the quadratic formula.
- In elementary algebra, the quadratic formula is a formula that gives the solution(s) to a quadratic equation.
- x = [-b±√b²-4ac]/2a
- x = [-(-5) ± √25 - 4(1)(-36)]/2(1)
- x = (5 ± √25 + 144)/2
- x = (5 ± √169)/2
- x = (5 ± 13)/2
- x = 9 or x = -4
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