What is the discriminant of 9x2 2 10x?
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be sure what the question was. For a quadratic equation of the form
y = ax^2 + bx + c, where a, b and c are real numbers and a is
non-zero, the discriminant is b^2 – 4ac.
Note that the equation must first be written with descending powers of x so as to identify a, b and c.
Using the discriminant how many times does the graph of this equation cross the x-axis 5x squared -10x-2 equals 0?
How do you prove that the line y equals 2x plus 1.25 is a tangent to the curve y squared equals 10x?
The discriminant in the quadratic equation x2 + 11x + 121 = x + 96 is 0. Simplify the equation to the form Ax2 + Bx + C = 0 and you get x2 + 10x + 25 = 0. The discriminant is B2 - 4AC or 100 - (4)(1)(25) or 100 - 100 or 0. Not asked, but answered for completeness - since the discriminant is 0, there is one real solution, namely x…
If the discriminant b2-4ac of the quadratic equation equals zero then it will have two equal roots meaning that the line is tagent to the curve. So by implication: (2x+1.25)(2x+1.25) = 10x 4x2-5x+25/16 = 0 Hence use the discriminant of b2-4ac :- (-5)2-4*4*25/16 = 0 Therefore the discriminant equals 0 so the line will be tangent to the curve. In fact working out the equation gives x having two equal roots of 5/8
What are three ways of proving that the line of y equals 2x plus 5 over 4 is a tangent to the curve of y squared equals 10x showing work?
If: y = 2x+1.25 and y^2 = 10x Then: (2x+1.25)^2 = 10x So: 4x^2 +5x+1.5625 = 10x => 4x^2 -5x+1.5625 = 0 Proof 1: The discriminant of the quadratic equation = 0 Proof 2: The solutions of the quadratic both equal 5/8 Proof 3: Plot the line of y = 2x+5/4 and the curve of y^2 = 10x on the Cartesian plane which will result in a contact point of (5/8, 5/2) making the line…
Y2=10X and Y=2x+5 will never touch each other. If there is a touch point then there will be a common value (Touch point) of x and y which will satisfy both equations. But there is no common point so it is not possible Improved Answer: equation 1: y = 2x++5/4 => y2 = 4x2+5x+1.5625 when both sides are squared equation 2: y2 = 10x By definition: 4x2+5x+1.5625 = 10x => 4x2-5x+1.5625 = 0 If the…
What is the value of k when the line y equals kx plus 1.25 is a tangent to the curve y squared equals 10x?
Equations: y = kx +1.25 and y^2 = 10x If: y = kx +1.25 then y^2 = (kx +1.25)^2 =>(kx)^2 +2.5kx +1.5625 So: (kx)^2 +2.5kx +1.5625 = 10x Transposing terms: (kx)^2 +2.5kx +1.5625 -10x = 0 Using the discriminant formula: (2.5k -10)^2 -4(1.5625*k^2) Multiplying out the brackets: 6.25k^2 -50k +100 -6.25^2 = 0 Collecting like terms: -50k +100 = 0 Solving the above equation: k = 2 Therefore the value of k is: 2
It can tell you three things about the quadratic equation:- 1. That the equation has 2 equal roots when the discriminant is equal to zero. 2. That the equation has 2 distinctive roots when the discriminant is greater than zero. £. That the equation has no real roots when the discriminant is less than zero.
What is the value of k when the line y equals 3x plus 1 is a tangent to the curve of y2 plus x2 equals k?
What facts concerning the solution of a quadratic equation can be deduced from the discriminant of the quadratic formula?
For a quadratic equation f(x) = ax^2 + bx + c we can use the discriminant to find out how many roots (answers) the equation has. To find this out we put it through b^2 - 4ac. If the answer is smaller than 0 (negative) then there are no real roots. If the answer is exactly 0 then there is one answer that is used twice. If the answer is bigger than 0 then the…