Question

For the polynomial 3x – 8x2 + 5, which of the following options is not correct?
1)parabola opens downward
2)parabola cuts the x-axis at two distinct points
3)parabola cuts the x-axis at one point
4)zeros are real

Answer 1

Answer:

For the polynomial 3x – 8x2 + 5, which of the following options is not correct?

1)parabola opens downward

2)parabola cuts the x-axis at two distinct points

3)parabola cuts the x-axis at one point

4)zeros are real

Step-by-step explanation:

Answer 2

Answer :

Option (3) .

Parabola cuts the x-axis at one point .

Note :

★ General form of the quadratic polynomial is given as ; y = ax² + bx + c .

★ Graph of a quadratic polynomial comes out to be parabola .

★ The discriminant , D of the quadratic polynomial y = ax² + bx + c is given by ;

D = b² - 4ac .

★ If D = 0 , then the zeros are real and equal .

→ The parabola touches the x-axis at a unique point .

★ If D > 0 , then the zeros are real and distinct .

→ The parabola cuts the x-axis at two distinct points .

★ If D < 0 , then the zeros are unreal (imaginary) .

→ The parabola would not cut the x-axis at any point .

★ If a > 0 , then the parabola is upwards .

★ If a < 0 , then the parabola is downwards .

★ If D < 0 and a < 0 , then y < 0 .

★ If D < 0 and a > 0 , then y > 0 .

★ If D > 0 , then y = 0 at two points .

★ If D = 0 , then y = 0 at one point .

Solution :

Here ,

The given quadratic polynomial is ;

y = 3x - 8x² + 5

Given quadratic polynomial in general form :

y = -8x² + 3x + 5

Comparing the given quadratic polynomial with general form y = ax² + bx + c ,

We have ;

a = -8

b = 3

c = 5

Clearly ,

a = -8 , ie. a < 0

Thus ,

• The parabola of the given quadratic polynomial will be downwards .

Now ,

The discriminant of the given quadratic polynomial will be ;

=> D = b² - 4ac

=> D = 3² - 4×(-8)×5

=> D = 9 + 160

=> D = 169 (D > 0)

Clearly ,

D = 169 , ie. D > 0

Thus ,

• The zeros of the given given quadratic polynomial are real and distinct .

• The parabola of the given quadratic polynomial will cut the x-axis at two distinct points .

Hence ,

The statement which is not correct for the given quadratic polynomial is ;

• Parabola cuts the x-axis at one point .