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]