Rewrite each of the statements as a conjunction of two if-then statements. This quadratic equation has two distinct real roots if, and only if, its discriminant is greater than zero.

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: Check the definiteness of the following quadratic form; Q(x1, X2, X3) = 2xỉ + 3x – xỉ + 5x,x3 + x,X3

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Q: If a quadraticequation has two distinct real roots, what does this say about its discriminant?

A: correct ans is C. for real and district root,discriminant must be graterthan zero.

Q: Create a cubic expression that when divided by (x-1) will have a remainder of 6

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Q: Show that the roots of px2 + (p - q)x - q = 0 are real for all real values of p and q.

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Q: If the roots of the equation x - 8x + a² - 6a = distinct, then find all possible values of a.

A: Since the roots of the given equation are real and distinct, We must have…

Q: Solve the following quadratic using any method we've learned. X-16x + 63 = 0

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Q: Check the definiteness of the following quadratic form;

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Q: A. Find the sum and product of the solutions of the following quadratic equations. Quadratic…

A: sum of root =-b/a product of root =c/a

Q: For which values ​​of a does the equation 3x³-5x²-4x+a=0 have exactly x=3? Determine all real roots…

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Q: Determine the type of the quadrilateral of this equation, for every a belongs to Real numbers 2x² -…

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Q: Find the four roots of ( 3+14)

A: The given problem is related with complex analysis. We have to find the four roots of 3 + i4. Note…

Q: 1.Solve the following polynomial equations.  a)  2X2+1=x2+2X

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Q: Check the definiteness of the following quadratic form; Q(x1, X2, X3) = 2xỉ + 3x – x + 5x,x3 + X2X3

A: The definiteness of quadratic form is defined by corresponding symmetric matrix.

Q: The roots of (x + 1)2 + 1 = 0 are

A: NOTE: Refresh your page if you can't see any equations. . subtract 1 from both sides

Q: Use the quadratic formula to solve for x. 9x+ 5x–1=0 (If there is more than one solution, separate…

A: We have given equation 9x2+5x-1=0 Then, comparing this ax2+bx+c=0 we have a=9,b=5,c=-1 Now, using…

Q: If the age of Ali is bigger than Sara in which the addition of age of Ali and Sara is equal (24 +…

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Q: n 10x + 11y = n has

A: The equation as, ax+by=S. The smallest positive integer S is expressed as, S=(k+1)*a*b

Q: Determine the roots of the following quadratic expression 4x² - 19x + 12 = 0 a) x=3 and x=-16 b) x =…

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Q: If the discriminant of a quadratic equation is 0, then the equation has

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Q: Find the values of k for which the equation x? – 4x + k = 0 has distinct real roots.

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Q: Will “the domain and range of a quadratic equation will be [-∞, ∞]”? Why?

A: The general form of a quadratic equation is ax2+bx+c=0 where a, b, c are known scalars with a≠0. We…

Statements and Logic

Logic is the analysis of general patterns of thoughts without regard to any specific sense of context.