- How many solutions does x 2 12x 36 have?
- What is the discriminant of x2 12x 36 0?
- What is the nature of the roots of the equation x 2 12x 36 0?
- What is the discriminant of the 3x 2 x 2 0?
- What are the zeros of f/x )= x 2 x 20?
- What are the zeros of f/x )= x x 7?
- Is x 8 a factor of the function f/x )=- 2x 3?
- How are turning points calculated?
- Is a root a turning point?
- How many turning points does a quartic function have?
- Can a quartic have 2 turning points?
- Can a quartic function have 2 turning points?
- Can a fourth degree polynomial have 2 turning points?

## How many solutions does x 2 12x 36 have?

Solve Quadratic Equation by Completing The Square 3.2 Solving x2-12x+36 = 0 by Completing The Square . This quadratic equation has one solution only.

## What is the discriminant of x2 12x 36 0?

Hence, for the quadratic equation x2 – 12x + 36 = 0, we get only one real and equal root, which is 6….Discriminant.

Discriminant value Cases | Roots of quadratic | Factorisation of quadratic |
---|---|---|

Discriminant value = 0 | two identical real roots | two identical linear factors |

## What is the nature of the roots of the equation x 2 12x 36 0?

Hence roots are equal.

## What is the discriminant of the 3x 2 x 2 0?

Complete step-by-step answer: It is given that the discriminant of 3×2+2x+a=0 is double the discriminant of x2−4x+2=0. This is a linear equation in terms of a. We will solve this linear equation to find the value of a. ∴ We get the value of a as −13.

## What are the zeros of f/x )= x 2 x 20?

Answer: The zeroes of the given function are -5 and 4.

## What are the zeros of f/x )= x x 7?

Answer: The zeroes of the given function are 0 and 7.

## Is x 8 a factor of the function f/x )=- 2x 3?

No. When the function f(x) = −2×3 + 17×2 − 64 is divided by x − 8, the remainder is zero. Therefore, x − 8 is not a factor of f(x) = −2×3 + 17×2 − 64.

## How are turning points calculated?

Use the symmetry of the graph to find the coordinates of the turning point of the following quadratic:

- y = x 2 − 3 x + 2 y=x^2-3x+2 y=x2−3x+2. [3 marks]
- x 2 − 3 x + 2 = ( x − 1 ) ( x − 2 ) x^2-3x+2=(x-1)(x-2) x2−3x+2=(x−1)(x−2) Setting this equal to zero gives.
- ( x − 1 ) ( x − 2 ) = 0 (x-1)(x-2)=0 (x−1)(x−2)=0.

## Is a root a turning point?

The point at which it turns is a turning point, and this will be either a minimum or a maximum value. The turning point for this graph is at (0, -3). For any quadratic there may be two roots, one root (actually the same root repeated), or no roots (the graph does not cross y = 0.

## How many turning points does a quartic function have?

Higher degree

Type of polynomial | Number of x-intercepts | Number of turning points |
---|---|---|

linear | 1 | 0 |

quadratic | from 0 to 2 | 1 |

cubic | from 1 to 3 | 0 or 2 |

quartic | from 0 to 4 | 1 or 3 |

## Can a quartic have 2 turning points?

Cubic polynomials have a degree of 3 whereas quartic polynomials have a degree of 4. Cubic graphs will have zero or two turning points. Quartic graphs will have one or three turning points.

## Can a quartic function have 2 turning points?

This can only happen if there are an odd number of turning points. Similarly, for odd n the sign as x→∞ is the opposite of the sign as x→−∞, so there must be an even number of turning points.

## Can a fourth degree polynomial have 2 turning points?

Fourth degree polynomials are also known as quartic polynomials. Quartics have these characteristics: Zero to four roots. Zero, one or two inflection points.