Question

solve the following using quadratic formula X square - 15 X + 50 is equal to zero​

Answer 1

Question :-

Solve the following quadratic equation using the quadratic formula - x² - 15x + 50 = 0.

Answer :-

→ x = 5 or 10

Solution :-

We have ,

→ f(x) → x² - 15x + 50 =0 .....eq.(1)

We know that ,if we have any quadratic equation

f(x) = ax² + bx + c = 0 .....eq.(2)

then the quadratic formula is :

$\mapsto \bf \: x = \frac{ - b \pm \sqrt{ {b}^{2} - 4ac} }{2a}$

Now,

Comparing eq.(1) and eq.(2)

→ a = 1 , b = -15 and c = 50 ,

now apply the above quadratic formula -

$\to \sf x = \frac{ - ( - 15) \pm \sqrt{ {( - 15)}^{2} - 4 \times 50} }{2 } \\ \\ \to \sf x = \frac{15 \pm \sqrt{225 - 200} }{2} \\ \\ \to \sf \: x = \frac{15 \pm \sqrt{25} }{2} \\ \\ \to \sf \: x = \frac{15 \pm5}{2} \\ \\ \star \sf \: \: case \: (1) \: if \: \\ \to \sf \: x = \frac{15 + 5}{2} \\ \\ \to \: \sf x = \frac{20}{2} \\ \\ \to \: \boxed{\sf \: x = 10} \\ \\ \sf \star \: \: case \: (2) \: if \: \\ \\ \to \sf \: x = \frac{15 - 5}{2} \\ \\ \to \sf \: x = \frac{10}{2} \\ \\ \to \boxed{ \sf x = 5}$

Hence ,x = 5 or 10

▬▬▬▬▬▬▬▬▬▬▬▬

Verification :-

• If x = 5,

→ f(5) = (5)² - 15×5 + 50 = 0

→ 25 - 75 + 50 = 0

→ 25 - 25 = 0

→ 0 = 0

• If x = 10

→ f(10) = (10)² - 15×10 + 50 = 0

→ 100 - 150 + 50 = 0

→100 - 100 = 0

→ 0 = 0

Hence verified .

▬▬▬▬▬▬▬▬▬▬▬▬

Answer 2

Answer:

${x}^{2} - 15x + 50 = 0 \\ x = \frac{ - b± \sqrt{ {b}^{2} - 4ac } }{2a} \\ x = \frac{ - ( - 15)± \sqrt{ {( - 15)}^{2} - 4 \times 1 \times 50 } }{2 \times 1} \\ x = \frac{15± \sqrt{225 - 200} }{2} \\ x = \frac{15± \sqrt{25} }{2} \\ x = \frac{15±5}{2} \\ x = \frac{15 + 5}{2} \: \: \: or \: \: \: x = \frac{15 - 5}{2} \\ x = \frac{20}{2} \: \: \: or \: \: \: x = \frac{10}{2} \\ \boxed{ \large x = \underline{ \underline{ 10}} \: \: \: or \: \: \: x = \underline{ \underline{5}}}$