Question

Solution of a quadratic equation X^2+5x-6=0

Answer 1

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Solution of a quadratic equation x^2+5x-6=0

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Given

• A polynomial
• X^2+5x-6=0

To Find

• Factors of the polynomial
• Relationship between coefficient

Explanation:

${x}^{2} + 5x - 6 = 0$

⭐️We have to split the middle term such a way that the product become -6 and sum become 5x⭐️

${x}^{2} + 5x - 6 = 0$

${x}^{2} + 6x -x - 6 = 0$

$x(x + 6) - 1(x + 6)$

$(x + 6)(x - 1)$

$x = 1 \: \: - 6$

Additional information:

Let the zeros of the polynomial be Alpha and Beta.

so

$\alpha + \beta = \frac{ - b}{a}$

$\alpha \times \beta = \frac{c}{a}$

Here,

a=1

b=5

c= -6

$\alpha + \beta = \frac{ - 5}{1}$

$\alpha + \beta = \frac{ - coefficient \: of \: x}{coefficient \: of \: {x}^{2} }$

and

$\alpha \times \beta = \frac{ - 6}{1}$

$\alpha \times \beta = \frac{constant \: term}{coefficient \: of \: {x}^{2} }$

Hence relation verified //:

• A quadratic equation is an equation of second degree meaning it contains at last one term that is squared.

• The standard form of ax^2+bx+c=0 with a,b,c being constants or numerical coefficients and x is an unknown variable.

Answer 2

Step-by-step explanation:

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