How do you use the discriminant to determine the nature of the solutions given $–7q^2 + 8q + 2 = 0$ ?

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Answer 1 · 2017-09-05T10:57:24

Two real solutions , $q ~~ 1.35(2dp) , q ~~ -0.21(2dp)$

$-7q^2+8q+2=0$ Comparing with standard quadratic equation

$ax^2+bx+c=0$ , here $a= -7 ,b=8 ,c=2, D= b2 - 4ac$

$= 8^2+4*7*2 =120$ is called the "discriminant". If $D$ is positive,

we get two real solutions, if it is zero we get just one solution, and

if it is negative we get complex solutions. Here $D$ is positive so

we will get two real solutions. $q= (- b +- sqrt D)/(2a)$ or

$q= (- 8 +- sqrt 120)/(-14) or q= 4/7 +- (sqrt 30)/7 :.q =1/7(4+-sqrt30)$

or $q ~~ 1.35(2dp) , q ~~ -0.21(2dp)$ [Ans]

How do you use the discriminant to determine the nature of the solutions given –7q^2 + 8q + 2 = 0 –7q^2 + 8q + 2 = 0?