Question

What is the nature of root of the quadratic
equation 2 x²-3x-4=0​

Answer 1

$Compare \: given \: Quadratic \: equation$

$2x^{2}-3x-4=0 \:with \: ax^{2}+bx+c=0 , we$

$get$

$a = 2 ,b = -3 \:and \: c = -4$

$Discriminant (D) = b^{2} - 4ac$

$= (-3)^{2} - 4 \times 2 \times (-4)$

$= 9 + 32$

$= 41$

$\green { \gt 0 }$

Therefore.,

$\green { Roots \: are \: real \: and \: distinct .}$

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Answer 2

Answer:

real and unequal roots

Step-by-step explanation:

$\text{Given quadratic equation,} \\ 2x^2-3x-4=0 \\\\ It \ is \ of \ the \ form \ ax^2+bx+c=0 \\\\ => a=2,b=-3,c=-4 \\\\ \text{nature of the roots is known by discriminant,D} \\\\ \boxed{\bf D=b^2-4ac} \\\\ => D=(-3)^2-4(2)(-4) \\ =>D=9+32\\ =>D=41 > 0 \\\\ \text{It has real and unequal roots}$

NATURE OF ROOTS :

If D < 0 ; no real roots

If D = 0 ; real and equal roots

If D > 0 ; real and unequal roots