# Chapter 1 - Section 1.2 - Quadratic Equations - 1.2 Assess Your Understanding: 73

no real solution

#### Work Step by Step

RECALL The nature of solutions using the quadratic equation $ax^2+bx+c=0$ can be determined using the value of its discriminant $b^2-4ac$. If the value of the discriminant is: (1) negative, then the equation has no real solutions; (2) zero, then the equation has one repeated solution; and (3) positive, then there are two unequal solutions. The given quadratic equation has: $a=2 \\b=-6 \\c=7$ Solve for the discriminant to obtain: $=b^2-4ac \\=(-6)^2-4(2)(7) \\=36-56 \\=-20$ The discriminant is negative, so the equation has no real solutions.

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