For what value of x the expression x 2 5x 14 is positive?
For what value of x the expression x 2 5x 14 is positive?
Hence for x∈(−∞,−2)∪(2,∞), the expression x2−5x−14 is positive.
Do you agree that x2 5x 14 0 and 14 5x x2 0 have the same solutions?
No it does not have the same solution. Firstly, because x²+5x-14=0 and -x²-5x+14=0 are two different equations.
What is the product of the solutions of the expression x2 5x 14 0?
Factor x 2 – 5x – 14 = 0 to (x – 7)(x + 2) = 0; therefore, the solutions (the values of x that make this true) are 7 and -2. Their product: 7 × -2 = -14. Also, note than in the standard formula ax 2 + bx + c, the product of the solutions will always be .
Which of the equations has two solutions Why?
quadratic equation
Do you agree that not all quadratic equations can be solved by factoring?
No, not all quadratic equations can be solved by factoring. This is because not all quadratic expressions, ax2 + bx + c, are factorable.
Can every quadratic equation be solved?
Yes every quadratic can be solved by factoring. That’s what the quadratic formula is telling us. Whether a quadratic can be factored with integer or rational coefficients is a bit more difficult.
Can all quadratic equations be solved?
Don’t be fooled: Not all quadratic equations can be solved by factoring. For example, x2 – 3x = 3 is not solvable with this method. One way to solve quadratic equations is by completing the square; still another method is to graph the solution (a quadratic graph forms a parabola—a U-shaped line seen on the graph).
Can you use the quadratic formula for any quadratic equation?
The Quadratic Formula can be used to solve any quadratic equation of the form ax2 + bx + c = 0. The form ax2 + bx + c = 0 is called standard form of a quadratic equation. Before solving a quadratic equation using the Quadratic Formula, it’s vital that you be sure the equation is in this form.
Can a quadratic equation have 1 root?
Thus, a parabola has exactly one real root when the vertex of the parabola lies right on the x-axis. The simplest example of a quadratic function that has only one real root is, y = x2, where the real root is x = 0.
Can you only have 1 imaginary zero?
No. If there is an imaginary root, then the complex conjugate of that root is also a root. So if there is one complex zero, then there is another.
Can a quadratic have 3 roots?
Theorem : A quadratic equation cannot have more than two roots. Proof : Let us consider α,β and γ are the three roots of the given quadratic equation ax2 a x 2 + bx + c = 0, where a,b,c ϵ R and a \ne 0. Then each α,β and γ will satisfy this quadratic equation.