Solve the equation [tex]2x^{2} - 5x - 7 = 0[/tex] using the quadratic formula. Then write [tex]2x^{2} - 5x - 7[/tex] in the form [tex]a(x - r_{1})(x - r_{2})[/tex].
Answer (2)
2 x 2 + 2 x − 7 x − 7 = 2 x ( x + 1 ) − 7 ( x + 1 ) = ( 2 x − 7 ) ( x + 1 ) = = 2 ( x − 3.5 ) ( x + 1 ) 2 x 2 − 5 x − 7 = 0 ⇔ 2 ( x − 3.5 ) ( x + 1 ) = 0 x − 3.5 = 0 ∨ x + 1 = 0 . x = 3.5 x = − 1
To solve the equation 2 x 2 − 5 x − 7 = 0 using the quadratic formula, we find the roots to be x 1 = 3.5 and x 2 = − 1 . The equation can be factored as 2 ( x − 3.5 ) ( x + 1 ) .
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