Question

Find the discriminate of 1)2x²-5√2x+4=0
2)√3x²+2√2x-2√3=0​

Answer 1

Answer:

2x² – 5x + 3 = 0

On comparing the given equation with ax² + bx + c = 0

Here, a = 2 , b = -5 and c = 3

D(discriminant) = b² – 4ac

D = (-5)² –  4 x 2 x 3

D =  25 – 24 = 1

D = 1

Hence the discriminant of the quadratic equation 2x² – 5x + 3 = 0 is 1.

2) Given :  x² + 2x + 4 = 0

On comparing the given equation with ax² + bx + c = 0

Here, a = 1 , b = 2 and c = 4

D(discriminant) = b² – 4ac

D = (2)² – 4 x 1 x 4

D = 4 – 16 = – 12

D = -12

Hence,the discriminant of the quadratic equation x² + 2x + 4 = 0 is = – 12.

3)  Given : (x -1) (2x -1) = 0

(x -1) (2x -1) = 0

2x² - x - 2x + 1 = 0

2x² - 3x + 1 = 0

On comparing the given equation with ax² + bx + c = 0

Here,  a =  2 , b = -3 , c = 1

D(discriminant) = b² – 4ac

D = (-3)² – 4 x 2 x 1

D =  9 – 8 = 1

D = 1

Hence,the discriminant of the quadratic equation (x -1) (2x -1) = 0 is = 1

4) Given :  x² – 2x + k = 0

On comparing the given equation with ax² + bx + c = 0

Here,  a = 1 , b = -2 , and c = k

D(discriminant) = b² – 4ac

D = (-2)²  –  4(1)(k)

D= 4 – 4k

Hence the discriminant of the quadratic equation x² – 2x + k = 0 is (4 – 4k)

5)  Given :  3√x²  + 2√2x–2√3 = 0

On comparing the given equation with ax² + bx + c = 0

Here, a = √3 ,b = 2√2 and c = −2√3

D(discriminant) = b² – 4ac

D = (2√2)² –(4× √3 × -2√3)

D  = 8 + 24 = 32

D = 32

Hence the discriminant of the quadratic equation 3√x²  + 2√2x–2√3 = 0 is 32.

6)  Given : x² – x + 1 = 0

On comparing the given equation with ax² + bx + c = 0

Here,  a =1 , b = -1 and  c = 1

D(discriminant) = b² – 4ac

D = (-1)² – 4 x 1 x 1

D = 1 – 4 = – 3

D = - 3

Hence the discriminant of the quadratic equation x² – x + 1 = 0 is - 3.

Answer 2

Answer:

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