What are the roots of the following equations?1. x^2 + 7x + 10 = 02. 2x^2 + 8x - 10 = 03. x (x +3) = 284. x^2 - 8x +15 = 05. x^2 - 10x + 25 = 0​

Note:sana makatulong :3Answer:1. x = -5 or x = -22. x = 1 or x = -53. x = -7 or x = 44. x = 5 or x = 35. x = 5Solution:1.[tex] {x}^{2} + 7x + 10 = 0[/tex][tex](x + 5)(x + 2) = 0[/tex][tex]x + 5 = 0 \: \: \: \: \: or \: \: \: \: \: x + 2 = 0[/tex][tex]x = - 5 \: \: \: \: \: or \: \: \: \: \: x = - 2[/tex]2.[tex] {2x}^{2} + 8x - 10[/tex]Using Formula:[tex]x = \frac{ - b + - \sqrt{ {b}^{2} - 4ac } }{2a} [/tex]Substitute:[tex] \frac{ - 8 + - \sqrt{ {8}^{2} - 4(2)( - 10)} }{2(2)} [/tex][tex] \frac{ - 8 + - \sqrt{64 + 80} }{4} [/tex][tex] \frac{ - 8 + - \sqrt{144} }{4} [/tex][tex] \frac{ - 8 + - 12}{4} [/tex]1[tex] \frac{ - 8 + 12}{4} = \frac{4}{4} = 1[/tex]2. [tex] \frac{ - 8 - 12}{4} = \frac{ - 20}{4} = - 5[/tex][tex]x = 1 \: \: \: \: \: or \: \: \: \: \: x = - 5[/tex]3.[tex]x(x +3 ) = 28[/tex][tex] {x}^{2} + 3x = 28[/tex][tex] {x}^{2} + 3x - 28 = 0[/tex][tex](x + 7)(x - 4) = 0[/tex][tex]x + 7 = 0 \: \: \: \: \: or \: \: \: \: \: x - 4 = 0[/tex][tex]x = - 7 \: \: \: \: \: or \: \: \: \: \: x = 4[/tex]4.[tex] { {x}^{2} - 8x + 15 = 0}[/tex][tex](x - 5)(x - 3) = 0[/tex][tex]x - 5 = 0 \: \: \: \: \: or \: \: \: \: \: x - 3 = 0[/tex][tex]x = 5 \: \: \: \: \: or \: \: \: \: \: x = 3[/tex]5.[tex] {x}^{2} - 10x + 25 [/tex][tex](x - 5)(x - 5) = 0[/tex][tex]x - 5 = 0[/tex][tex]x = 5[/tex]

Answered by rajirajaq | 2024-09-07