Тема: I need help with some quadratic equations?

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Entering your problem is easy to do. Just type!.

Your problem will appear on a Web page exactly the way you enter it here. You can wrap a word in square brackets to make it appear bold. For example [my story] would show as my story on the Web page containing your problem.

TIP: Since most people scan Web pages, include your best thoughts in your first paragraph.

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The quadratic equation x 2 − 6 x + 9 = 0 has double roots of x = 3 (both roots are the same)

For the time being, we shall deal only with quadratic equations that can be factored (factorised). If you need a reminder on how to factor, go back to the section on Factoring Trinomials.

Entering your problem is easy to do. Just type!.

Your problem will appear on a Web page exactly the way you enter it here. You can wrap a word in square brackets to make it appear bold. For example [my story] would show as my story on the Web page containing your problem.

TIP: Since most people scan Web pages, include your best thoughts in your first paragraph.

Do you have some pictures or graphics to add? Great! Click the button and find the first one on your computer. Select it and click on the button to choose it.

Then click on the link if you want to upload up to 3 more images.

The quadratic equation x 2 − 6 x + 9 = 0 has double roots of x = 3 (both roots are the same)

For the time being, we shall deal only with quadratic equations that can be factored (factorised). If you need a reminder on how to factor, go back to the section on Factoring Trinomials.

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a million. permit the form of 5c funds be x. hence, the form of 10c funds is 3x, and the form of 25c funds is (3x + 2). the completed value of the 5c funds is 0.05x, the completed value of 10c funds is 0.3x and the completed value of 25c funds is (0.25)(3x + 2) = 0.75x + 0.5 as a result the completed value of all funds is = 0.05x + 0.3x + 0.75x + 0.5 = a million.1x + 0.5 all of us comprehend that a million.1x + 0.5 = 4.ninety, so we ve: a million.1x = 4.4 x = 4 as a result there are 4 5c funds, twelve 10c funds and fourteen 25c funds. 2) permit the quantity invested in the corporate be x and the quantity put in the mark downs financial business enterprise be y. x + y = 2500 y= 2500 - x --- (a million) (0.06)x + (0.05)y = 141 --- (2) utilising (a million) and (2), we ve: (0.06)x + (0.05)(2500 - x) = 141 0.06x + one hundred twenty five - 0.05x = 141 6x + 12500 - 5x = 14100 x = 1600 because x = 1600, y = 2500 - 1600 = 900 as a result, he invested $1600 in the corporate and $900 in the financial business enterprise. 3) After a million.5 hr, the bus travelled: (a million.5)(50) = seventy 5 miles The bus is travelling at 50mph, while the motor vehicle is travelling at 75mph. hence, each and every hour, the motor vehicle won seventy 5 - 50 = 25 miles over the bus. Distance between bus and vehicle on the beginning up = seventy 5 miles. Time mandatory to overhaul bus = seventy 5 / 25 = 3 hr Time stunning now = 4am + a million.5 hr = 5.30am Time whilst vehicle overtake bus = 5.30am + 3hr = 8.30am 4) permit the form of rooms rented on the beginning up be x. permit the unique value of room be y. hence, we ve: 28800 = xy y = 28800 / x --- (a million) The form of rooms rented now could be (x + 6). the value now could be (y - 20). the completed quantity earned proceed to be unchanged, so we ve: 28800 = (x + 6)(y - 20) --- (2) Substituting (a million) into (2), we can get: 28800 = (x + 6)((28800 / x) - 20) 28800x = (x + 6)(28800 - 20x) 28800x = -20x^2 + 28680x + 172800 20x^2 + 120x - 172800 = 0 x^2 + 6x - 8640 = 0 (x - ninety)(x + ninety six) = 0 x = ninety or x =-ninety six (Rejected, because value won t be ready to be unfavourable). as a result, ninety rooms have been rented out on the beginning up on the unique value. 5) permit the unique velocity be x. New velocity = (x + 5) hence, we ve: (20 / x) + (20 / (x + 5)) = a million 20(x + 5) + 20x = x(x + 5) 20x + a hundred + 20x = x^2 + 5x x^2 - 35x - a hundred = 0 utilising the quadratic formulation, we ve: x = [35 +/- sqrt((-35)^2 + 4(a hundred))] / 2 x = (35/2) +/- (a million/2)sqrt(1625) the value won t be ready to be unfavourable, so the unique velocity would desire to be (35/2) + (a million/2)sqrt(1625) km/hr