The roots of the quadratic equation are - 2 - √10 and - 2 + √10, respectively. The first root lies between - 6 and - 5 and the second root lies between 1 and 2.
According to the statement, the quadratic equation x² + 2 · x - 6 = 0 has no integer roots and we must determine between what integers the two roots lie. First, we proceed to find the roots of the polynomial:
x² + 2 · x - 6 = 0 Given
x² + 2 · x + 4 = 10 Compatibility with addition / Associative, commutative and modulative property / Definition of addition and subtraction
(x + 2)² = 10 Perfect square trinomial
x + 2 = ± √10 Definition of square root
x = - 2 ± √10 Compatibility with addition / Existence of additive inverse / Associative and modulative property / Result
The roots of the quadratic equation are - 2 - √10 and - 2 + √10, respectively. The first root lies between - 6 and - 5 and the second root lies between 1 and 2.
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