Question

determine the natural of the root of the quadratic equation 2x²-3x-=4=0​

Answer 1

Answer:

2x²-3x-4=0

to find the nature if roots first we have to find the discriminant of given equation

a=2,b=-3,c=-4

discriminant =b²-4ac

=(-3)²-4(2)(-4)

=9+32

=41>0

to fins the nature there are 3 conditions

• D>0(2 real and distinct roots)
• D=0(2 real and equal roots )
• D<0(no roots )

so, according to 3 conditions we came to know that the above equation have 2 real and distinct roots

to find the roots there is one another formula

$x = \frac{ - b + or - \sqrt{d} }{2a} \\ x = \frac{- 2 + or - \sqrt{41} }{4} \\ x = \frac{ - 2 + \sqrt{41} }{4} or \: x = \frac{ - 2 - \sqrt{41} }{4}$

Step-by-step explanation:

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