Question

If both the zeros of a quadratic polynomial x square +mx+9 are equal find the value of m​

Answer 1

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▪️Let α and β be the roots of quadratic polynomial.

▪️Given, α = β

Given, α = β      ▪️  Quadratic polynomial - x² + mx + 9

▪️a = 1, b = m, c = 9.

▪️Sum of roots, α + β =  -b/a = -m/1  ------------ [1]

▪️product of roots, αβ = c/a  = 9 ----------- [2]

▪️Since α = β, [2] becomes

▪️α² = 9

▪️=> α = ±3

▪️Substitute the value of α in [1],

▪️α + β = -m

▪️2α = - m ( since α = β)

▪️=> if α = + 3 then  m =  - 6

=> if α = + 3 then  m =  - 6   if α = - 3, then m = + 6

▪️Thus value of m is ±6

Hopes it help you✌️✌️

Answer 2

EXPLANATION.

• GIVEN

both the zeroes of a quadratic equation

x^2 + mx + 9 = 0

To find value of M

according to the question,

we can find discriminant

a = 1 , b = m, c = 9

=> D = b^2 - 4ac = 0

=> D = 0

=> ( m) ^2 - 4(1) (9) = 0

=> m^2 - 36 = 0

=> m^2 = 36

=> m = + 6 or m = - 6

Some related formula of quadratic equation.

$1) = d \: = {b}^{2} - 4ac$

$2) = x = \frac{ - b \pm \: \sqrt{d} }{2a}$

3) = D > 0 = Roots are real and unequal.

4) = D = 0 = Roots are real and equal.

5) = D < 0 = Roots are imaginary.