Question

x2 - (m - 3)x + m = 0 find the value of m​

Answer 1

${\bold{\underline{\underline{Answer:}}}}$

${\bold{\therefore m=1\:and\:9}}$

${\bold{\underline{\underline{Step-by-step\:explanation:}}}}$

$\underline \bold{Given : } \\ \implies {x}^{2} - (m - 3)x + m = 0 \\ \\ \underline \bold{To \: Find : } \\ \implies Value \: of \: m = ?$

• According to given question :

$\bold{By \: quadratic \: formula : } \\ \implies D= {b}^{2} - 4ac = 0 \:\:\:\bold{(equal\:roots)}\\ \\ \implies (m - 3)^{2} - 4 \times 1 \times m = 0 \\ \\ \implies {m}^{2} + {3}^{2} - 2 \times m \times 3 - 4m = 0 \\ \\ \implies {m}^{2} + 9 - 6m - 4m = 0 \\ \\ \implies {m}^{2} - 10m + 9 = 0 \\ \\ \bold{Using \: middle \: term \: spliting : } \\ \implies {m}^{2} - 9m - m + 9 = 0 \\ \\ \implies m(m - 9) - 1(m - 9) = 0 \\ \\ \implies (m - 1)(m - 9) = 0 \\ \\ \bold{\implies m = 1 \: and \: 9 }$

Answer 2

Correct Question:

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

Solution:

Given Equation:

=> x² - (m - 3)x + m = 0

When b² - 4ac = 0, then only roots are equal. So,

=> b² - 4ac = 0

Here, a = x², b = -(m - 3) and c = m

So, put the value in above condition we get,

=> [-(m - 3)]² - 4 × 1 × m = 0

=> (m + 3)² - 4m = 0

=> m² + 9 - 6m - 4m = 0

=> m² + 9 - 10m

Now, By using splitting middle term method.

=> m² - 10m + 9 = 0

=> m² - 9m - m + 9 = 0

=> m( m - 9) - 1(m - 9) = 0

=> (m - 1) (m - 9)

=> m = 1 and 9

So, value of m is 1 and 9.