An equation is known as a quadratic equation provided that the degree of the equation must be 2 that means the power of the degree deciding variable must be two. The representation for a quadratic equation is given as ax2+bx+c=0 where a,b and c are the real constant numbers...
When a trinomial has a leading coefficient of 1 (i.e., a monic polynomial)— as is in this case — all the $\Box$s reduce to 1, which simplifies the search a bit: \begin{equation*}(x + a)(x + b) = x^2+13x + 36 \end{equation*} To explore a bit, we can expand the ...
C. Questions that require solutions9 Use suitable methods to solve the following quadratic equations in one variable:(1) (3x+1)^2=4 ;(2) x^2-4x-60=0 ;(3) 5(x-3)^2+x=3 ;(4) 5x^2-2x-7=0 ;(5) 1/2x-1=2x^2 ;(6) 3x^2+2√3x+1=0 ;(7) 3(x-2)^2=x^2-2x ;...
= (-3)2 - 4(5)(8) = 9 - 160 = -151The discriminant is -151, a negative number. So the equation 5x2 - 3x + 8 = 0 has no real number solutions.Example 2Use the discriminant to determine the nature of the solutions of this quadratic equation: 9x2 - 6x = -1Solution...
To solve the problem, we need to analyze the given equation and determine the conditions under which it represents an ellipse. The equation is: (5x−1)2+(5y−2)2=(λ2−2λ+1)(3x+4y−1)2 Step 1: Rewrite the equationWe can rewrite the left-hand side of the equation as: (...
Graph the quadratic function, 3(x)^2+5x+9. Graph the quadratic function: y = -(x + 1)^2 + 3. Graph the quadratic function: y = (x - 1)(x - 4). Graph the quadratic function: y = -(x + 1)(x - 4). Which of the following quadratic functions has a graph which co...
{eq}x^2 + 9x - 14 = 0 {/eq} Quadratic Equation: In the quadratic equation, the solution can be identified by completing the square means converting the particular quadratic equation can be converted into algebraic identities like {eq}{\left( {a + b} \right)^2} = {a^2} + {b^2...
Struggling With Quadratic Equations? Get Allen’s Free Practice Tests Free ALLEN Tests Text SolutionVerified by Experts The correct Answer is: ∴ the roots are 2,2,1,1,-3 | ShareSave Answer Step by step video, text & image solution for Find the repeated roots of x^5-3x^4-5x^3+27x^...
−3x2+13x+10=0 Question: Find the solution to the equation below. Quadratic Equation: An equation in which the highest power of the variable is two is known as a quadratic equation and its general form isax2+bx+c=0. To find the solution of the quadratic equation, we have...
) is a quadratic in x with \Delta :=225-408t^2+208t^4>0,\ t\in (0,1), it has two roots, namely \begin{aligned} x_i= x_i(t) = \frac{ 3+4t^2 + (-1)^{i+1} \sqrt{ 225-408t^2+208t^4 }}{ 24t }, \quad i=1,2. \end{aligned} (34) a. Let x=x_1. ...