Question

Find the value of 'm' so that the equation has equal roots (m-3)x²-4x+1=0

Answer 1

EXPLANATION.

=> The equation has equal roots

=> ( m - 3 )x² - 4x + 1 = 0

To find the value of m.

=> Equation has real and equal roots.

=> D = 0 or b² - 4ac = 0

=> ( m - 3 )x² - 4x + 1 = 0

=> ( -4)² - 4 ( m - 3 )(1) = 0

=> 16 - 4m + 12 = 0

=> 28 - 4m = 0

=> m = 7

Therefore,

value of m = 7.

SOME RELATED FORMULA.

1) = D > 0 roots are real and unequal.

2) = D = 0 roots are real and equal.

3) = D < 0 roots are imaginary.

Answer 2

Answer:

✡ Given ✡

$\leadsto$ The equation has equal roots (m-3)x²- 4x + 1 = 0.

✡ To Find ✡

$\leadsto$ What will be the value of m.

✡ Formula Used ✡

⭐ b² - 4ac = 0 ⭐

✡ Solution ✡

➡ (m-3)x² - 4x + 1

where, a= (m-3), b= -4, c= 1

Therefore,

The discriminate = b²-4ac = 0

$\implies$ (-4)² - 4.(m-3).1 = 0

$\implies$ 16 - 4m + 12 = 0

$\implies$ -4m = -12 +16

$\implies$ -4m = -28

$\implies$ m = $\dfrac{28}{4}$

$\implies$ m = 7 > 0

Therefore, The two roots of the given quadratic equation are real and unequal.

_________________________

⭐ Additional Information ⭐

$\leadsto$ The two roots of the quadratic equation ax²+bx+c = 0[a≠0]

(1) real and equal if b²-4ac = 0

(2) real and unequal if b²-4ac > 0

(3) no real root if b²-4ac < 0

Step-by-step explanation:

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