Math, asked by chrissanta8411, 5 days ago

# find the value of discriminant of the equation x2-2x-7=0​

9

### EXPLANATION.

Equation ⇒ x² - 2x - 7 = 0.

### To find discriminant.

⇒ D = 0.  Or  b² - 4ac = 0.

⇒ (-2)² - 4(1)(-7) = 0.

⇒ 4 + 28 = 0.

⇒ D = 32.

Value of discriminant = 32.

### Descartes Rule of Signs.

(1) = The number of almost positive roots of polynomial equation f(x) = 0. ( arranged in decreasing order of the degree ) can not exceeds the number of changes of signs in f(x) = 0 as we move from left to right.

(2) = The number of almost negative roots of a polynomial equation f(x) = 0. can not exceeds the number of changes of signs in f(-x).

25

### Discriminant:-

Discriminant is helps to find nature of roots.

We can find Discriminant through :-

In Quadratic equation ax² +bx + c

Discriminant is determined by b² -4ac

Discriminant is denoted by D

### Now lets find Discriminant !!

Given Q.E x²-2x -7 =0

a = 1

b = -2

c = -7

We know that

D = b²-4ac

D = (-2)² -4 (1)(-7)

D = 4 + 28

D = 32

So, Discriminant of Given Quadratic equation is

### Know more:-

If D=0 roots are real and equal

D>0 roots are real and distinct

D<0 roots are complex and conjugate

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