The graph of a quadratic function intercepts the x-axis in two places and the y-axis in one place. According to the fundamental theorem of algebra, which of the following statements is correct?

Q: If a, b, and c are constructible, show that the real roots of ax2 + bx + care constructible.

A: We know the roots of ax2+bx+c=0 are given by x=-b±b2-4ac2a

Q: Express as a polynomial.

A: To express 13a2+4b13a2-4b as a polynomial. Solution: We have identity a+ba-b=a2-b2. Using the above…

Q: Find all the solutions to the polynomial: x* + 4x°+7x² + 16x + 12 = 0 1 -4 -2i O 2i -3 O -1

A: A polynomial function is a function that involves only non-negative integer powers or only positive…

Q: Consider the polynomial (x − a)(x − b) and the real number line shown.(a) Identify the points on the…

A: Given:           (x−a)(x−b)

Q: a. Rewrite the polynomial 2x² + x in standard form. ° +-7x + 1 b., What is the leading coefficient?…

A:

Q: Factorise the following quadratic: f(x)=x2−72f(x)=x2−72 Select one: f(x)=(x+7)(x-7) f(x)=(x-7)(x-7)…

A: The given equation is, f(x)=x2-72 The objective is to factorize f(x) Use the following identity…

Q: Identify the function that matches the graph except at x = 2. 5 4 3 2 1- -54-3 -2 -1 -1 -2 + --4 + 1…

A: Since you have posted multiple questions i can do first question as per our company guidelines…

Q: For any real number xx the maximum value of 4−6a−a2 is, 4 7 9 13

A:

Q: Give an example of a quadratic function that has only real zeros and an example of one that has only…

A: Quadratic functions have two zeroes. Since complex zeroes always appear in pairs, there will be…

Q: A research finds that the more couples argue, the less intimate they tend to feel towards each…

A: From the above data  We are given that A research finds that the more couples argue, the less…

Q: Determine the different possibilities for the numbers of positive, negative, and nonreal complex…

A: Given is  f(x) =5x^5 -2x^4 -4x^3 +2x^2-9x-4

Q: how is the irrational zero found?

A:

Q: Write out a careful proof of the fact that the square of an odd number is odd.

A:

Q: Classify the quadratic forms as positive definite, positive semidefinite, negative definite,…

A: To classify the quadratic form x1^2 + x2^2 - x3^2 + 4x1x2, we will use the following steps: Step 1:…

Q: Factor completely. (x - 5)-1/2(x + 5)-1/2- (x + 5)1/2(x - 5)-3/2

A: factor: x-5-12x+5-12-x+512x-5-32

Q: A baseball is "popped" straight up by a batter. The height of the ball above the ground is given by…

A:

Q: (x+1) is a factor of x²+2x²+2x+1 Find the other factor.

A: is a factor of .To find other factor.

Q: where it says "there are no changes in sign of each term, thus, there are no positive real roots,…

A: Step 1: Step 2: Step 3: Step 4:

Q: (a) Suppose we factor the polynomial a+25 as much as possible. Explain why there will be no linear…

A: (a) The given polynomial is : x4+25. We will apply the formula: a2-b2=(a+b)(a-b). We can factorize…

Q: Factor the following quadratic expression: 10x + 89x –9 O (10x + 1) (x – 9) O (10z – 1) (x + 9) | O…

A:

Roots

The main dissimilarity between real and complex roots is that the real roots are obtained as real numbers, in contrast with the complex roots, which are indicated as imaginary numbers. The standard format for depicting any complex number is in the form of a + bi.