Sage-Tips

What is the quadratic equation if the roots are 5 and 9?

The standard quadratic equation using the given set of solutions {5,9} is y=x2−14x+45 y = x 2 – 14 x + 45 .

What is the formula for difference of roots of a quadratic equation?

Difference of two roots of a quadratic equation is : sqrt(D)/a which is not equal to D. Discriminant (D or Δ) or determinant just determines the nature of roots of a quadratic equation.

What is the difference between root and solution of an equation?

Zeros (roots) of a function are the values of x for which f(x)=0 while solutions are the values of the x which make the equation f(x) = c true where c is any constant . for example if f(a) = 0 then a is called root and (a,0) called solution of f(x) while if f(b) = c then (b,c) is called solution.

What is the quadratic equation of 6 and 3?

The standard quadratic equation using the given set of solutions {6,3} is y=x2−9x+18 y = x 2 – 9 x + 18 .

What is the quadratic equation of 8 and 10?

The standard quadratic equation using the given set of solutions {10,8} is y=x2−18x+80 y = x 2 – 18 x + 80 .

What is the quadratic equation of 5 and 7?

The standard quadratic equation using the given set of solutions {−5,7} is y=x2−2x−35 y = x 2 – 2 x – 35 .

What is the quadratic equation if the roots are 8 and 10?

The standard quadratic equation using the given set of solutions {−8,10} is y=x2−2x−80 y = x 2 – 2 x – 80 .

What is alpha and beta in quadratic equation?

We have seen that, in the case when a parabola crosses the x-axis, the x-coordinate of the vertex lies at the average of the intercepts. Thus, if a quadratic has two real roots α,β, then the x-coordinate of the vertex is 12(α+β). Now we also know that this quantity is equal to −b2a.

What kind of roots or solutions of the quadratic equation?

Let ax2 + bx + c = 0 be a quadratic equation. If aα2 + bα + c = 0 then α is called a root of the quadratic equation ax2 + bx + c = 0. If aα2 + bα + c = 0 then we say x = α satisfies the equation ax2 + bx + c = 0 and x = α is a solution. Thus, every solution is root.

What the difference is between roots solutions and zeros?

A root of an equation is a value at which the equation is satisfied. Roots the equation f(x)= x3+ x2– 3x – ex=0 are the x values of the points A, B, C and D. At these points, the value of the function becomes zero; therefore, the roots are called zeroes.