Write a quadratic equation whose solutions are [tex]7i[/tex] and [tex]-7i[/tex].
Answer (3)
The **quadratic equation **for which **solutions **will be 7i and -7i is x^{2} +49.
What is a quadratic equation?
Any **equation **that may be put into **standard **form is referred to as a quadratic equation in algebra . where a, b, and c are well-known numbers , x is an unknown value.
In general, it is **assumed **that a > 0; equations with a = 0 are thought to be degenerate since they become **linear **or even more basic. The **coefficients **of the equation are the numbers a, b, and c, which can be separated by referring to them as the quadratic coefficient , linear coefficient, and **constant **or free term, respectively.
As well as being **referred **to as the roots or **zeros **of the expression on the left-hand side of the equation , the values of x that satisfy it are known as **solutions **of the equation. There are only two **possible **answers to a quadratic equation .
Therefore, one can first write the **quadratic equation **in factored form (x-7i)(x+7i), as -7i and 7i are its solutions . The result of **multiplying **this is x^{2} +49.
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The quadratic equation with solutions 7i and -7i is x² + 49 = 0.
To write a quadratic equation whose solutions are 7i and -7i, we need to use the fact that if 'a' and 'b' are solutions to a quadratic equation of the form ax² + bx + c = 0, then the equation can be written as a(x - a)(x - b) = 0. In this case, the solutions are 7i and -7i, so we plot them in the form (x - 7i)(x + 7i), which simplifies to x² - (7i)². Since i² = -1, this further simplifies to x² + 49 = 0. This is the required quadratic equation with imaginary solutions.
The quadratic equation with solutions 7 i and − 7 i is x 2 + 49 = 0 . This is derived from the factored form of the quadratic equation based on its roots. The calculations show that the equation can be expressed as x 2 + 49 = 0 .
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