if the discriminant is zero then the quadratic has?
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The discriminant can be positive, zero, or negative, and this determines how many solutions there are to the given quadratic equation. A positive discriminant indicates that the quadratic has two distinct real number solutions. A discriminant of zero indicates that the quadratic has a repeated real number solution.
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The discriminant determines the nature of the roots of a quadratic equation. ... If Δ≥0, the expression under the square root is non-negative and therefore roots are real. For real roots, we have the following further possibilities. If Δ=0, the roots are equal and we can say that there is only one root.
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Answer and Explanation: When a quadratic equation, ax2 + bx + c = 0, has no b term, then it has the form ax2 + c = 0.
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Eigenvectors are by definition nonzero. Eigenvalues may be equal to zero. We do not consider the zero vector to be an eigenvector: since A 0 = 0 = λ 0 for every scalar λ , the associated eigenvalue would be undefined.
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The discriminant of a quadratic equation is given by d = b^2 - 4ac, where a is the coefficient of the quadratic term (x^2), b is the coefficient of the linear term (x) and c is the constant term. If the discriminant is a positive number, then the quadratic equation will have two real and distinct roots.
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Discriminant, in mathematics, a parameter of an object or system calculated as an aid to its classification or solution. In the case of a quadratic equation ax2 + bx + c = 0, the discriminant is b2 − 4ac; for a cubic equation x3 + ax2 + bx + c = 0, the discriminant is a2b2 + 18abc − 4b3 − 4a3c − 27c2.
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An equation of the form ax2 + bx + c = 0 where a, b, and c are constants and a ≠ 0 is known as a quadratic equation. Here, it is equating to 0. Examples:x2 - 4x + 3 = 0, x2 - 3x = 0 etc. a polynomial when equated to zero or some value becomes an equation.
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are linearly independent if and only if the determinant of the matrix formed by taking the vectors as its columns is non-zero. Since the determinant is non-zero, the vectors (1, 1) and (−3, 2) are linearly independent. Otherwise, suppose we have m vectors of n coordinates, with m < n.
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Equal or double roots. If the discriminant b2 - 4ac equals zero, the radical in the quadratic formula becomes zero. In this case the roots are equal; such roots are sometimes called double roots. Therefore, the roots are equal.
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An equation of the type ax 2 + bx + c = 0 where a, b and c all are real numbers and a and b. If b=0 then this equation becomes a pure quadratic equation. One example of an Adfected quadratic equation is 13x 2 -12x-1=0.
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Solving a quadratic equation means we find two values ( from the equation) which. give the value of the quadratic equation as zero on substitution . The two values. are also called as zeros of the polynomials. For example can be written as (x + 2 ) ( x + 3 ) = 0.
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Roots are also called x-intercepts or zeros. A quadratic function is graphically represented by a parabola with vertex located at the origin, below the x-axis, or above the x-axis. Therefore, a quadratic function may have one, two, or zero roots.
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['Quadratic Equation in Standard Form: ax2 + bx + c = 0.', 'Quadratic Equations can be factored.', 'Quadratic Formula: x = −b ± √(b2 − 4ac) 2a.', 'When the Discriminant (b2−4ac) is: positive, there are 2 real solutions. zero, there is one real solution. negative, there are 2 complex solutions.']
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Quadratic Equation with One Solution. The quadratic equation 4x squared, plus bx, plus 9, equals 0, has only one solution. ... That means that the discriminant, b squared minus 4ac, must be equal to 0.
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When x = 0. Then the domain is "all x not equal to zero". The domain doesn't care what is in the numerator of a rational expression. The domain is only influenced by the zeroes of the denominator.
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The zeros of the function are where the f(x) = 0. These functions can have 0, 1, or 2 real zeros. There are several techniques for finding the zeros of a quadratic function, including the square root property, factoring, completing the square, and the quadratic formula.
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∵α and β are the zeroes of above polynomial. Hence, -1 is the correct answer.